How would you begin to solve for x in this exponential equation? 3 x − 1 = 24 3^{x-1}=24 3 x − 1 = 2 4 Select 3 appropriate beginning steps.

log ⁡ ( 3 x − 1 ) = log ⁡ ( 24 ) \log\left(3^{x-1}\right)=\log\left(24\right) lo g ( 3 x − 1 ) = lo g ( 2 4 )

log ⁡ 3 ( 3 x − 1 ) = log ⁡ 3 ( 24 ) \log_3\left(3^{x-1}\right)=\log_3\left(24\right) lo g 3 ( 3 x − 1 ) = lo g 3 ( 2 4 )

ln ⁡ ( 3 x − 1 ) = ln ⁡ ( 24 ) \ln\left(3^{x-1}\right)=\ln\left(24\right) ln ( 3 x − 1 ) = ln ( 2 4 )

3 x − 1 3 = 24 3 \frac{3^{x-1}}{3}=\frac{24}{3} 3 3 x − 1 = 3 2 4

Solve for x in the exponential equation. e x + 6 + 5 = 1 e^{x+6}+5=1 e x + 6 + 5 = 1 Round your answer to the nearest hundreth.

x + 6 = ln ⁡ ( − 4 ) , T h e r e f o r e n o s o l u t i o n x+6=\ln\left(-4\right),\ \ Therefore\ no\ solution x + 6 = ln ( − 4 ) , T h e r e f o r e n o s o l u t i o n

x + 6 = ln ⁡ 6 , T h e r e f o r e x = − 4.21 x+6=\ln6,\ \ Therefore\ x=-4.21 x + 6 = ln 6 , T h e r e f o r e x = − 4 . 2 1

x + 6 = ln ⁡ ( 4 ) , T h e r e f o r e x = − 4.61 x+6=\ln\left(4\right),\ \ Therefore\ x=-4.61 x + 6 = ln ( 4 ) , T h e r e f o r e x = − 4 . 6 1

ln ⁡ e x + 11 = 1 , T h e r e f o r e x = − 10 \ln e^{x+11}=1,\ \ Therefore\ x=-10 ln e x + 1 1 = 1 , T h e r e f o r e x = − 1 0

Solve for the exact value of x in the exponential equation. 5 x = 3 x + 2 5^x=3^{x+2} 5 x = 3 x + 2 Then approximate your answer to the nearest hundreth.

x = log ⁡ 9 log ⁡ ( 5 3 ) , T h e r e f o r e x = 4.30 x=\frac{\log9}{\log\left(\frac{5}{3}\right)},\ \ Therefore\ x=4.30 x = lo g ( 3 5 ) lo g 9 , T h e r e f o r e x = 4 . 3 0

x = 2 log ⁡ 3 ( log ⁡ 5 − log ⁡ 3 ) , T h e r e f o r e x = 1.32 x=\frac{2\log3}{\left(\log5-\log3\right)},\ \ Therefore\ x=1.32 x = ( lo g 5 − lo g 3 ) 2 lo g 3 , T h e r e f o r e x = 1 . 3 2

x = 2 log ⁡ 3 ( log ⁡ 5 − 3 ) , T h e r e f o r e n o s o l u t i o n x=\frac{2\log3}{\left(\log5-3\right)},\ \ Therefore\ no\ solution x = ( lo g 5 − 3 ) 2 lo g 3 , T h e r e f o r e n o s o l u t i o n

x = 2 log ⁡ 3 ( log ⁡ 5 − 3 ) , T h e r e f o r e x = 3.17 x=\frac{2\log3}{\left(\log5-3\right)},\ \ Therefore\ x=3.17 x = ( lo g 5 − 3 ) 2 lo g 3 , T h e r e f o r e x = 3 . 1 7

Solve for the exact value of x in the exponential equation. 7 2 x + 1 = 3 x 7^{2x+1}=3^x 7 2 x + 1 = 3 x Then approximate your answer to the nearest hundreth.

x = log ⁡ ( 1 7 ) log ⁡ ( 49 3 ) , T h e r e f o r e x = − . 70 x=\frac{\log\left(\frac{1}{7}\right)}{\log\left(\frac{49}{3}\right)},\ \ Therefore\ x=-.70 x = lo g ( 3 4 9 ) lo g ( 7 1 ) , T h e r e f o r e x = − . 7 0

x = log ⁡ 3 log ⁡ 7 − 1 2 , T h e r e f o r e x = − . 22 x=\frac{\frac{\log3}{\log7}-1}{2},\ \ Therefore\ x=-.22 x = 2 lo g 7 lo g 3 − 1 , T h e r e f o r e x = − . 2 2

x = − log ⁡ 7 2 ( log ⁡ 7 − log ⁡ 3 ) , x = − 1.15 x=\frac{-\log7}{2\left(\log7-\log3\right)},\ \ x=-1.15 x = 2 ( lo g 7 − lo g 3 ) − lo g 7 , x = − 1 . 1 5

x = 2 log ⁡ 3 ( log ⁡ 7 − 3 ) , T h e r e f o r e x = 3.17 x=\frac{2\log3}{\left(\log7-3\right)},\ \ Therefore\ x=3.17 x = ( lo g 7 − 3 ) 2 lo g 3 , T h e r e f o r e x = 3 . 1 7

Solve for the exact value of x in the exponential equation. 2 x − 1 = 3 x + 1 2^{x-1}=3^{x+1} 2 x − 1 = 3 x + 1 Then approximate your answer to the nearest hundreth.

x = log ⁡ ( 6 ) log ⁡ ( 2 3 ) , T h e r e f o r e x = − 4.42 x=\frac{\log\left(6\right)}{\log\left(\frac{2}{3}\right)},\ \ Therefore\ x=-4.42 x = lo g ( 3 2 ) lo g ( 6 ) , T h e r e f o r e x = − 4 . 4 2

x = log ⁡ 3 − log ⁡ 2 log ⁡ 2 − log ⁡ 3 , T h e r e f o r e x = − 1 x=\frac{\log3-\log2}{\log2-\log3},\ \ Therefore\ x=-1 x = lo g 2 − lo g 3 lo g 3 − lo g 2 , T h e r e f o r e x = − 1

x = log ⁡ 6 ( log ⁡ 2 − log ⁡ 3 ) , T h e r e f o r e x = 4.26 x=\frac{\log6}{\left(\log2-\log3\right)},\ \ Therefore\ x=4.26 x = ( lo g 2 − lo g 3 ) lo g 6 , T h e r e f o r e x = 4 . 2 6

x = 2 log ⁡ 3 ( log ⁡ 2 − log ⁡ 3 ) , T h e r e f o r e x = − 5.42 x=\frac{2\log3}{\left(\log2-\log3\right)},\ \ Therefore\ x=-5.42 x = ( lo g 2 − lo g 3 ) 2 lo g 3 , T h e r e f o r e x = − 5 . 4 2

6.62pc MQ Solving Exponential Equations using Logs

Quiz

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Easy

•

CCSS

HSF.LE.A.4

Standards-aligned

Shayla Bushhousen

Used 13+ times

FREE Resource

13 questions

Show all answers

1.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

How would you begin to solve for x in this exponential equation?

$3^{x-1}=24$

Select 3 appropriate beginning steps.

$\log\left(3^{x-1}\right)=\log\left(24\right)$

$\log_3\left(3^{x-1}\right)=\log_3\left(24\right)$

$\ln\left(3^{x-1}\right)=\ln\left(24\right)$

$\frac{3^{x-1}}{3}=\frac{24}{3}$

2.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Which of the following is NOT a correct step toward the solving of this exponential equation?

$2e^{3x}=16$

$\frac{2e^{3x}}{2}=\frac{16}{2}$

$\ln\left(e^{3x}\right)=\ln\left(8\right)$

$3x=\ln\left(8\right)$

$x=\ln\left(\frac{8}{3}\right)$

3.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$7^x=12$

Round your answer to the nearest hundreth.

Tags

CCSS.HSF.LE.A.4

4.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$4^{2x}=32$

Round your answer to the nearest hundreth.

Tags

CCSS.HSF.LE.A.4

5.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$4^x-5=12$

Round your answer to the nearest hundreth.

Tags

CCSS.HSF.LE.A.4

6.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$8^{x+1}=3$

Round your answer to the nearest hundreth.

7.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$10^{3x}-1=5$

Round your answer to the nearest hundreth.

Tags

CCSS.HSF.LE.A.4

8.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$6-e^{12x}=5.2$

Round your answer to the nearest hundreth.

9.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$5e^{6x+3}=0.1$

Round your answer to the nearest hundreth.

Tags

CCSS.HSF.LE.A.4

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for x in the exponential equation.

$e^{x+6}+5=1$

Round your answer to the nearest hundreth.

$x+6=\ln6,\ \ Therefore\ x=-4.21$

$x+6=\ln\left(4\right),\ \ Therefore\ x=-4.61$

$x+6=\ln\left(-4\right),\ \ Therefore\ no\ solution$

$\ln e^{x+11}=1,\ \ Therefore\ x=-10$

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6.62pc MQ Solving Exponential Equations using Logs

13 questions

How would you begin to solve for x in this exponential equation? 3x−1=243^{x-1}=243x−1=24 Select 3 appropriate beginning steps.

Which of the following is NOT a correct step toward the solving of this exponential equation? 2e3x=162e^{3x}=162e3x=16

Solve for x in the exponential equation. 7x=127^x=127x=12 Round your answer to the nearest hundreth.

Solve for x in the exponential equation. 42x=324^{2x}=3242x=32 Round your answer to the nearest hundreth.

Solve for x in the exponential equation. 4x−5=124^x-5=124x−5=12 Round your answer to the nearest hundreth.

Solve for x in the exponential equation. 8x+1=38^{x+1}=38x+1=3 Round your answer to the nearest hundreth.

Solve for x in the exponential equation. 103x−1=510^{3x}-1=5103x−1=5 Round your answer to the nearest hundreth.

Solve for x in the exponential equation. 6−e12x=5.26-e^{12x}=5.26−e12x=5.2 Round your answer to the nearest hundreth.

Solve for x in the exponential equation. 5e6x+3=0.15e^{6x+3}=0.15e6x+3=0.1 Round your answer to the nearest hundreth.

Solve for x in the exponential equation. ex+6+5=1e^{x+6}+5=1ex+6+5=1 Round your answer to the nearest hundreth.

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Discover more resources for Mathematics

How would you begin to solve for x in this exponential equation?

$3^{x-1}=24$

Select 3 appropriate beginning steps.

Which of the following is NOT a correct step toward the solving of this exponential equation?

$2e^{3x}=16$

Solve for x in the exponential equation.

$7^x=12$

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

$4^{2x}=32$

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

$4^x-5=12$

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

$8^{x+1}=3$

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

$10^{3x}-1=5$

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

$6-e^{12x}=5.2$

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

$5e^{6x+3}=0.1$

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

$e^{x+6}+5=1$

Round your answer to the nearest hundreth.