Answer
$\left\{2\right\}$
Work Step by Step
Using the properties of logarithms, the given equation, $
\log_8 64=x
$, is equivalent to
\begin{align*}
\log_8 8^2&=x
\\
2\log_8 8&=x
&(\text{use }\log_b x^y=y\log_b x)
\\
2(1)&=x
&(\text{use }\log_b b=1)
\\
2&=x
.\end{align*}
Hence, the solution set of the equation $
\log_8 64=x
$ is $
\left\{2\right\}
$.
