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College Algebra : Solving Logarithmic Functions

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Example Questions

Example Question #56 : Exponential And Logarithmic Functions

Solve this logarithmic equation: ln(2x-2)=5

Possible Answers:

x=72.5

x=52.7

x=75.2

x=27.5

None of these.

Correct answer:

x=75.2

Explanation:

ln(2x-2)=5

Exponentiate:

$e^{ln2x-2}=e^5$

Add two to both sides:

$2x-2=e^5\rightarrow 2x=e^5+2$

Divide both sides by 2:

$x=\frac{e^5}{2}+1=\boldsymbol{75.2}$ (rounded answer)

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Example Question #11 : Solving Logarithmic Functions

$\log_{5}x=3$

Possible Answers:

$\frac{1}{25}$

$\frac{1}{125}$

125

Correct answer:

125

Explanation:

To solve this equation, remember log rules

$\log_{b}x=y; b^{y}=x$ .

This rule can be applied here so that

5^3=x

and

125=x.

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Example Question #12 : Solving Logarithmic Functions

Solve for x:

$log_{3}x=2$

Possible Answers:

x=6

x=4

x=9

x=2

Correct answer:

x=9

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{3}x=2$

$3^{2}=x$

x=9

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Example Question #13 : Solving Logarithmic Functions

Solve for x:

$log_{8}x=6$

Possible Answers:

x=48

$x=6^{8}$

x=262,144

x=728

Correct answer:

x=262,144

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{8}x=6$

$8^{6}=x$

x=262,144

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Example Question #13 : Solving Logarithmic Functions

Solve for x:

$log_{5}x=3$

Possible Answers:

x=8

x=15

x=25

x=125

Correct answer:

x=125

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{5}x=3$

$5^{3}=x$

x=125

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Example Question #63 : Exponential And Logarithmic Functions

Solve for x:

$log_{2}x=8$

Possible Answers:

x=128

x=256

x=1024

x=512

Correct answer:

x=256

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{2}x=8$

$2^{8}=x$

x=256

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Example Question #64 : Exponential And Logarithmic Functions

Solve for x:

$log_{10}x=4$

Possible Answers:

x=1,000

x=100

x=10,000

x=100,000

Correct answer:

x=10,000

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{10}x=4$

$10^{4}=x$

x=10,000

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Example Question #65 : Exponential And Logarithmic Functions

Solve for x:

$log_{14}x=2$

Possible Answers:

x=169

x=196

x=136

x=28

Correct answer:

x=196

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{14}x=2$

$14^{2}=x$

x=196

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Example Question #14 : Solving Logarithmic Functions

Solve for x:

$log_{6}x=3$

Possible Answers:

x=216

x=18

x=36

x=9

Correct answer:

x=216

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{6}x=3$

$6^{3}=x$

x=216

Report an Error

Example Question #65 : Exponential And Logarithmic Functions

Solve for x:

$log_{6}x=4$

Possible Answers:

x=36

x=216

x=1296

x=24

Correct answer:

x=1296

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{6}x=4$

$6^{4}=x$

x=1296

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College Algebra : Solving Logarithmic Functions

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #56 : Exponential And Logarithmic Functions

Example Question #11 : Solving Logarithmic Functions

Example Question #12 : Solving Logarithmic Functions

Example Question #13 : Solving Logarithmic Functions

Example Question #13 : Solving Logarithmic Functions

Example Question #63 : Exponential And Logarithmic Functions

Example Question #64 : Exponential And Logarithmic Functions

Example Question #65 : Exponential And Logarithmic Functions

Example Question #14 : Solving Logarithmic Functions

Example Question #65 : Exponential And Logarithmic Functions

All College Algebra Resources

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