Write the equation in logarithmic form. 8 3 = 512 8^{3\ }=\ 512 8 3 = 5 1 2

log ⁡ 8 512 = 3 \log_8\ 512\ =\ 3 lo g 8 5 1 2 = 3

log ⁡ 3 8 = 512 \log_38=512 lo g 3 8 = 5 1 2

log ⁡ 8 3 = 512 \log_8\ 3=512 lo g 8 3 = 5 1 2

log ⁡ 3 512 = 8 \log_3\ 512\ =\ 8 lo g 3 5 1 2 = 8

6 log ⁡ 8 u − 2 log ⁡ 8 v 6\log_8\ u\ -\ 2\log_8v 6 lo g 8 u − 2 lo g 8 v

6 log ⁡ 8 v − 2 log ⁡ 8 u 6\log_8\ v\ -\ 2\log_8u 6 lo g 8 v − 2 lo g 8 u

3 log ⁡ 8 u − 2 log ⁡ 8 v 3\log_8\ u\ -\ 2\log_8\ v 3 lo g 8 u − 2 lo g 8 v

6 log ⁡ 8 u − log ⁡ 8 v 6\log_8\ u\ -\log_8v 6 lo g 8 u − lo g 8 v

5 log ⁡ 5 a − 30 log ⁡ 5 b 5\log_5\ a-30\log_5\ b 5 lo g 5 a − 3 0 lo g 5 b

5 log ⁡ 5 a − 6 log ⁡ 5 b 5\log_5\ a-6\log_5\ b 5 lo g 5 a − 6 lo g 5 b

5 log ⁡ 5 a + 30 log ⁡ 5 b 5\log_5\ a+30\log_5\ b 5 lo g 5 a + 3 0 lo g 5 b

30 log ⁡ 5 b − 5 log ⁡ 5 a 30\log_5\ b-5\log_5\ a 3 0 lo g 5 b − 5 lo g 5 a

6 log ⁡ 4 u − 36 log ⁡ 4 v 6\log_4\ u-36\log_4\ v 6 lo g 4 u − 3 6 lo g 4 v

log ⁡ 4 u − 6 log ⁡ 4 v \log_4\ u-6\log_4\ v lo g 4 u − 6 lo g 4 v

6 log ⁡ 4 u + 36 log ⁡ 4 v 6\log_4\ u+36\log_4\ v 6 lo g 4 u + 3 6 lo g 4 v

6 log ⁡ 4 u ÷ 36 log ⁡ 4 v 6\log_4\ u\ \div36\log_4\ v 6 lo g 4 u ÷ 3 6 lo g 4 v

log ⁡ 7 x + log ⁡ 7 y + 4 log ⁡ 7 z \log_7\ x+\log_7\ y+4\log_7\ z lo g 7 x + lo g 7 y + 4 lo g 7 z

4 log ⁡ 7 x + 4 log ⁡ 7 y + 4 log ⁡ 7 z 4\log_7\ x+4\log_7\ y+4\log_7\ z 4 lo g 7 x + 4 lo g 7 y + 4 lo g 7 z

log ⁡ 7 x − log ⁡ 7 y − 4 log ⁡ 7 z \log_7\ x-\log_7\ y-4\log_7\ z lo g 7 x − lo g 7 y − 4 lo g 7 z

4 log ⁡ 7 x y z 4\log_7\ xyz 4 lo g 7 x y z

4 log ⁡ u + 16 log ⁡ v 4\ \log\ u\ +16\log\ v 4 lo g u + 1 6 lo g v

4 log ⁡ u + 8 log ⁡ v 4\ \log\ u\ +8\log\ v 4 lo g u + 8 lo g v

4 log ⁡ u + 4 log ⁡ v 4\ \log\ u\ +4\log\ v 4 lo g u + 4 lo g v

4 log ⁡ u − 16 log ⁡ v 4\ \log\ u\ -16\log\ v 4 lo g u − 1 6 lo g v

Expand log ⁡ x y z \log x\ \sqrt{yz} lo g x y z <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

log ⁡ x + 1 2 log ⁡ y + 1 2 log ⁡ z \log\ x\ +\frac{1}{2\ }\log\ y\ +\frac{1}{2}\log\ z lo g x + 2 1 lo g y + 2 1 lo g z

1 2 log ⁡ x + 1 2 log ⁡ y + 1 2 log ⁡ z \frac{1}{2}\log\ x\ +\frac{1}{2\ }\log\ y\ +\frac{1}{2}\log\ z 2 1 lo g x + 2 1 lo g y + 2 1 lo g z

log ⁡ x − 1 2 log ⁡ y − 1 2 log ⁡ z \log\ x\ -\frac{1}{2}\log\ y\ -\frac{1}{2}\log\ z lo g x − 2 1 lo g y − 2 1 lo g z

log ⁡ x + 1 2 log ⁡ y + log ⁡ z \log\ x\ +\ \frac{1}{2\ }\log\ y\ +\log\ z lo g x + 2 1 lo g y + lo g z

Condense 3 log ⁡ 5 − 1 2 log ⁡ 25 3\log5-\frac{1}{2}\log\ 25 3 lo g 5 − 2 1 lo g 2 5

log ⁡ 1.2 \log\ 1.2 lo g 1 . 2

log ⁡ 15 25 \log\ \frac{15}{25} lo g 2 5 1 5

Expand and Condense Logarithms

Authored by Julie Wiseheart

Mathematics

10th - 11th Grade

CCSS covered

Used 66+ times

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25 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Write equation in exponential form.
$\log_2\ 128=7$

$7^2=128$

$2^{7\ }=\ 128$

$128^{2\ }=\ 7$

$2^{128\ }=\ 7$

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Write equation in exponential form.

$\log_3\frac{1}{27}=-3$

$-3^3\ =\ \frac{1}{27}$

$\frac{1}{27}^3=-3$

$3^{\frac{1}{27}}=-3$

$3^{-3}=\frac{1}{27}$

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Write the equation in logarithmic form.

$4^4=256$

$\log_4\ 4\ =\ 256$

$\log_{256}\ 4\ =\ 4$

$\log_4\ 256\ =\ 4$

$\log\ 4\ =\ 256$

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Write the equation in logarithmic form.

$8^{3\ }=\ 512$

$\log_38=512$

$\log_8\ 512\ =\ 3$

$\log_8\ 3=512$

$\log_3\ 512\ =\ 8$

Tags

CCSS.HSF.BF.B.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Expand

$6\log_8\ v\ -\ 2\log_8u$

$6\log_8\ u\ -\ 2\log_8v$

$3\log_8\ u\ -\ 2\log_8\ v$

$6\log_8\ u\ -\log_8v$

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Condense

$\log xyz^3$

$\log\ \frac{xy}{z^3}\$

$\log x\ +\ \log y\ +\ \log z^3$

$\log x^3y^3z^3$

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Expand

$\log_8\ x\ +\ \log_8\ y\ +\ \log_8\ z^5$

$\log_8\ x\ +\ \log_8\ y\ +\ 5\log_8\ z^{ }$

$\log_8\ xy\ +\ 5og_8\ z$

$5\log_8\ x\ +\ 5\log_8\ y\ +\ 5\log_8\ z^{ }$

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSF.LE.A.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Condense

$\log_8\ \frac{6x}{3y}$

$\log_8\ \frac{x^6}{y^3}$

$\log_8\ \frac{2x}{y}$

$\log_8\ 18xy$

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Expand

$5\log_5\ a-6\log_5\ b$

$5\log_5\ a-30\log_5\ b$

$5\log_5\ a+30\log_5\ b$

$30\log_5\ b-5\log_5\ a$

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

10.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Expand

$6\log_4\ u-36\log_4\ v$

$\log_4\ u-6\log_4\ v$

$6\log_4\ u+36\log_4\ v$

$6\log_4\ u\ \div36\log_4\ v$

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

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Expand and Condense Logarithms

Write equation in exponential form. log⁡2 128=7\log_2\ 128=7log2​ 128=7

Write equation in exponential form. log⁡3127=−3\log_3\frac{1}{27}=-3log3​271​=−3

Write the equation in logarithmic form. 44=2564^4=25644=256

Write the equation in logarithmic form. 83 = 5128^{3\ }=\ 51283 = 512

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Discover more resources for Mathematics

Write equation in exponential form.
$\log_2\ 128=7$

Write equation in exponential form.

$\log_3\frac{1}{27}=-3$

Write the equation in logarithmic form.

$4^4=256$

Write the equation in logarithmic form.

$8^{3\ }=\ 512$