Answer
$x=2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
2^x=\log_2 16
,$ use the properties of logarithms to simplify the right side. Then express both sides in the same base and equate the exponents.
$\bf{\text{Solution Details:}}$
Using exponents, the equation above is equivalent to
\begin{array}{l}\require{cancel}
2^x=\log_2 2^4
.\end{array}
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent
\begin{array}{l}\require{cancel}
2^x=4\log_2 2
.\end{array}
Since $\log_b b =1,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
2^x=4(1)
\\\\
2^x=4
\\\\
2^x=2^2
.\end{array}
Since the bases are the same, then the exponents can be equated. That is,
\begin{array}{l}\require{cancel}
x=2
.\end{array}
