Q. 10 - Precalculus Enhanced with Graphing Utilities

Question

Change the given exponential statement to an equivalent statement involving a logarithm.

$16=4^2$

Step-by-Step Solution

Answer

The equivalent logarithmic statement of the given exponential statement is $2={\log }_4\left(16\right)$

Step 1. Given information

An exponential equation is given as $16=4^2$

Step 2. Formula

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

Step 3. Simplification

The exponential statement is $16=4^2$.

Compare statement with $x=a^y$.

$x=16,a=4$, and $y=2$

So, the corresponding logarithmic statement is

$2={\log }_4\left(16\right)$