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All courses Algebra II · F-LE.4.2 38 of 55
Use the definition of logarithms to translate among logarithms in any base.

Rewrite a logarithmic equation in exponential form

Problem
What is the equivalent exponential form of \(\log_2(8)=3\)?
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Hint

Identify the base, the number inside the logarithm, and the value after the equals sign.

The definition logb(a)=c means bc=a. The value of the logarithm becomes the exponent in the exponential form.

Solution walkthrough

01

Recall the conversion definition

\[\log_b(A)=C~<->~b^C=A\]

A logarithm states the exponent C placed on base b to produce argument A.

02

Assign the three roles

\[\text{base}=2,~\text{exponent}=3,~\text{result}=8\]

In log base 2 of 8 equals 3, the subscript is the exponential base, the logarithm value is the exponent, and 8 is the power's result.

03

Write and verify the exponential form

\[2^3=8\]

Two multiplied by itself three times equals eight, confirming the equivalent exponential statement.

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Another way

  1. Read the logarithm aloud as: the exponent on 2 that produces 8 is 3.

!

Common mistake

Do not swap the argument and exponent. The log value 3 becomes the exponent, while 8 remains the result.

Solution walkthrough video