# How do you solve log_b 9=2?

Dec 10, 2015

$b = 3$
Change to the exponential form as explained below.

#### Explanation:

Given ${\log}_{b} 9 = 2$

Change this equation to its exponential form, since

${\log}_{a} x = y \iff {a}^{y} = x$

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

${b}^{2} = 9$
${b}^{2} = {3}^{2}$
$b = 3$

Remember, if the exponents are the same, then the answer is the base.