Answer
The solution of the equation is $\underline{-2+{{\log }_{3}}11}$
Work Step by Step
Consider the given equation:
${{3}^{x+2}}=11$
Take the logarithm of both sides and obtain:
$\log {{\left( 3 \right)}^{x+2}}=\log \left( 11 \right)$
Then use the multiplication and division rules of logarithmic functions to solve for x:
$\begin{align}
& \log {{\left( 3 \right)}^{x+2}}=\log \left( 11 \right) \\
& \left( x+2 \right)\log \left( 3 \right)=\log \left( 11 \right) \\
& \left( x+2 \right)=\log \left( \frac{11}{3} \right) \\
& \left( x+2 \right)={{\log }_{3}}11 \\
& x={{\log }_{3}}11-2 \\
& x=-2+{{\log }_{3}}11
\end{align}$
Thus the solution of the equation is $ x=-2+{{\log }_{3}}11$.
