Question

Change the given exponential statement to an equivalent statement involving a logarithm.
$9=3^2$

Short answer

The equivalent logarithmic statement of the given exponential statement is$2={\log }_{3}9$.

Step-by-step solution

Step 1. Given information

An exponential equation is given as$9=3^2$

Step 2. Formula

The exponential statement $x=a^y$ can be changed into a logarithmic function as$y={\log }_{a}x$

Step 3. Simplification

The exponential statement is$9=3^2.$

Compare statement with $x=a^y$.

$x=9,a=3$, and$y=2$

So, the corresponding logarithmic statement is

$2={\log }_{3}9$