Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 18

$x\approx-0.317$

Taking the logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $ 5^{x+2}=15 ,$ is \begin{array}{l}\require{cancel} \log5^{x+2}=\log15 \\\\ (x+2)\log5=\log15 \\\\ x+2=\dfrac{\log15}{\log5} \\\\ x=\dfrac{\log15}{\log5}-2 \\\\ x\approx-0.317 .\end{array}