Answer
$7$
Work Step by Step
Using exponents, the given expression, $
\log_2 128
$, is equivalent to
\begin{align*}\require{cancel}
\log_2 2^7
.\end{align*}
Using the properties of logarithms, the expression above is equivalent to
\begin{align*}\require{cancel}
&
7\log_2 2
&(\text{use }\log_b x^y=y\log_b x)
\\&=
7(1)
&(\text{use }\log_b b=1)
\\&=
7
.\end{align*}
Hence, the expression $
\log_2 128
$ evaluates to $
7
$.
