Answer
$x\approx1.7925$.
Work Step by Step
Taking the logarithm of both sides, the given equation, $
4^x=12
,$ is equivalent to
\begin{align*}
\log4^x&=\log12
.\end{align*}
Using the properties of logarithms and of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
x\log4&=\log12
&(\text{use }\log_bx^y=y\log_bx)
\\\\
\dfrac{x\cancel{\log4}}{\cancel{\log4}}&=\dfrac{\log12}{\log4}
\\\\
x&=\dfrac{\log12}{\log4}
.\end{align*}
Using a calculator to get the values of $\log12$ and $\log4$, then
\begin{align*}
x&\approx1.7925
.\end{align*}
Hence, the solution to $4^x=12$ is $x\approx1.7925$.
