Answer
$x=-1+\dfrac{\ln{24}}{\ln3}\approx 1.8928$
Work Step by Step
Take the natural logarithm of both sides to obtain:
\begin{align*}
\ln{\left(3^{x+1}\right)}&=\ln{24}\\\\
\end{align*}
Use the Power Rule of logarithms to obtain:
\begin{align*}
(x+1)\ln{3}&=\ln{24}\\\\
\frac{(x+1)\ln3}{\ln3}&=\frac{\ln{24}}{\ln3}\\\\
x+1&=\frac{\ln{24}}{\ln3}\\\\
x&=-1+\frac{\ln{24}}{\ln3}\\\\
x&\approx 1.8928
\end{align*}
