Answer
$x\approx1.404$
Work Step by Step
Taking the logarithm of both sides, the given equation, $
4^{x+1}=28
,$ is equivalent to
\begin{align*}
\log4^{x+1}&=\log28
.\end{align*}
Using the properties of logarithms, the equation above is equivalent to
\begin{align*}
(x+1)\log4&=\log28
&\left(\text{use }\log_ba^x=x\log_ba \right)
\\\\
\dfrac{(x+1)\log4}{\log4}&=\dfrac{\log28}{\log4}
\\\\
x+1&=\dfrac{\log28}{\log4}
\\\\
x+1-1&=\dfrac{\log28}{\log4}-1
\\\\
x&=\dfrac{\log28}{\log4}-1
\\\\
x&\approx1.404
.\end{align*}
Hence, the solution is $
x\approx1.404
.$
