#### Answer

$x\approx1.792$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
4^x=12
,$ take the logarithm of both sides. Then use the laws of logarithms to isolate the variable. Express the answer with $3$ decimal places.
$\bf{\text{Solution Details:}}$
Taking the logarithm of both sides, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\log4^x=\log12
.\end{array}
Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x\log4=\log12
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
\dfrac{x\log4}{\log4}=\dfrac{\log12}{\log4}
\\\\
x=\dfrac{\log12}{\log4}
\\\\
x\approx1.792
.\end{array}