Question

In the following exercises, solve each logarithmic equation.

${\log }_{a}16=2$

Short answer

The value is$a=4$

Step-by-step solution

Given information

Given equation${\log }_{a}16=2$

Rewrite in exponential form

Rewriting, we get

$$\begin{gathered} {\log }_{a}16=2 \\ {a}^2=16 \\ a=\pm 4 \end{gathered}$$

Checking the solution

Checking, we get

$$\begin{gathered} {\log }_4\left(16\right)={\log }_4\left(4^2\right) \\ =2{\log }_4\left(4\right) \\ =2 \end{gathered}$$

Base can't be negative so$a=-4$is eliminated