Question

solve the following logarithmic equation.
\log_{4}x = 2

select the correct choice below and fill in any answer boxes in your choice.

a. x = \square
(type an exact answer. use a comma to separate answers as needed.)

b. there is no solution.

Explanation:

Step1: Recall the logarithmic definition

The logarithmic equation $\log_{a}b = c$ can be converted to its exponential form $a^{c}=b$.
For the equation $\log_{4}x = 2$, here $a = 4$, $c=2$ and $b = x$.

Step2: Convert to exponential form

Using the definition, we get $4^{2}=x$.

Step3: Calculate $4^{2}$

We know that $4^{2}=4\times4 = 16$. So $x = 16$.

Answer:

A. $x = 16$