เลขชี้กำลังและลอการิทึม

$\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ย</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}^{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}$y=\left(\frac{1}{2}\right)^{-x} $$ย={\left(\frac{}{2}\right)}^{-x}$$ เป็นชั่วโมงเพิ่มหรือเป็นชั่วโมงลด

• เวลาเพิ่ม

• เวลาลด

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ย</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">0</span></span></span></span>}$y=\left(\frac{a}{1+a}\right)^x\ \ \ ;\ a>0 $$ย={\left(\frac{}{1+ก}\right)}^x;ก>0$$ เป็นรอบเพิ่มหรือรอบลด

• เวลาเพิ่ม

• เวลาลด

ค่ะ$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ฉ</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}^{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}$f\left(x\right)=3^{-x} $$ฉ\left(x\right)=3^{-x}$$ และ$\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">กรัม</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}$g\left(x\right)=2^x $$กรัม\left(x\right)=2^x$$ แล้ว$\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ฉ</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">กรัม</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$f\left(2\right)g\left(2\right) $$ฉ\left(2\right)กรัม\left(2\right)$$ มีค่าเท่าไร

• 9

• $\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">9</span></span></span></span>}}$\frac{1}{9} $$\frac{}{9}$$

• 4

ถ้า (-4, 16) ย้อนบนกราฟของ$\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ฉ</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}$f\left(x\right)=a^x $$ฉ\left(x\right)={ก}^x$$ เมื่อ${\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ง</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ฉ</span></span></span></span>}}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ร</span></span></span></span>}$D_f=อาร์ $${ง}_{}=R$$ แล้วมีค่าเท่าไหร่

• 16

• -16

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}$-\frac{1}{2} $$-\frac{}{2}$$

• $\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}$\frac{1}{2} $$\frac{}{2}$$

${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}^{\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}^{\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}}$3^{\frac{1}{2}}>3^{\frac{1}{3}} $$3^{\frac{}{2}}>3^{\frac{}{3}}$$ จริงหรือเป็นกรณี

• ความจริง

• เทียบ

${<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}^{\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(\frac{a}{1+a}\right)^{\frac{2}{3}}>\left(\frac{a}{1+a}\right) $${\left(\frac{}{1+ก}\right)}^{\frac{}{3}}>\left(\frac{}{1+ก}\right)$$ เมื่อ$\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">ก</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">0</span></span></span></span>}$ก>0 $$ก>0$$ จริงหรือเป็นกรณี

• ความจริง

• เทียบ

${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}$2^{x+3}>4\ $$2^{x+3}>4$$ ; x มีค่าเสมอ

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">,</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(-\infty,\ 4\right) $$\left(-\infty ,4\right)$$

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">,</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(-1,\ \infty\right) $$\left(-1,\infty \right)$$

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">,</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(1,\ \infty\right) $$\left(1,\infty \right)$$

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">,</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(-\infty,\ 1\right) $$\left(-\infty ,1\right)$$

${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">5</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">5</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">8</span></span></span></span>}}$5^{2x-2}>5^{x+8} $$5^{2x-2}>5^{x+8}$$ ; x มีค่าแค่ไหน

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">11</span></span></span></span>}$x>11 $$x>11$$

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"><</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">11</span></span></span></span>}$x<11 $$x<11$$

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">11</span></span></span></span>}$x>-11 $$x>-11$$

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"><</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">11</span></span></span></span>}$x<-11 $$x<-11$$

${<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}^{{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">8</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">27</span></span></span></span>}}$\left(\frac{2}{3}\right)^{x^2-2x}>\frac{8}{27} $${\left(\frac{}{3}\right)}^{x^2-2x}>\frac{}{27}$$ ; x มีคาม่าใดๆ

• [-1, 3]

• (-2, 3)

• (-1, 3)

• [1, 3]

เขียน${\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">16</span></span></span></span>}$\ 2^4=\ 16 $$2^4=16$$ รูปของลอการิทึมได้ตรงกับข้อใด

• 2=\log_{16}4 2 = แท้จริง ก 1 64

• 4=\log_216 4 = แท้จริง ก 21 6

• 16=\log_24 1 6 = แท้จริง ก 24

• 2=\log_416 2 = แท้จริง ก 41 6