Answer
FALSE
Work Step by Step
The left-hand expression, $
\log_2(64-16)
$, is equivalent to
\begin{align*}
&
\log_2 48
.\end{align*}
Using the properties of logarithms, the right-hand expression, $
\log_2 64-\log_2 16
$, is equivalent to
\begin{align*}
&
\log_2 \dfrac{64}{16}
&(\text{use }\log_b \dfrac{x}{y}=\log_b x-\log_b y)
\\\\&=
\log_2 4
.\end{align*}
Since $\log_2 48\ne\log_24$, then the given statement is false.
