Q. 17 - Precalculus Enhanced with Graphing Utilities

Question

Change the given logarithmic statement to an equivalent statement involving an exponent.

${\log }_2\left(8\right)=3$

Step-by-Step Solution

Answer

The equivalent exponential statement of the given logarithmic statement is $2^3=8$.

Step 1. Given information

A logarithmic statement is given as${\log }_2\left(8\right)=3$

Step 2. Formula

The logarithmic function $y={\log }_a\left(x\right)$ can be changed into an exponential statement as $x=a^y$.

Step 3. Conversion

The logarithmic statement is ${\log }_2\left(8\right)=3$.

Compare statement with $y={\log }_a\left(x\right)$.

$x=8, a=2$, and $y=3$

So, the corresponding exponential statement is

$2^3=8$