Practice Final Exam - Page 706: 57

$x=\dfrac{\log4-5\log3}{2\log3} \\\\\text{OR}\\\\ x\approx-1.8691 $

Taking the logarithm of both sides and using the properties of logarithms, the solution to the given equation, $ 3^{2x+5}=4 ,$ is \begin{array}{l}\require{cancel} \log3^{2x+5}=\log4 \\\\ (2x+5)\log3=\log4 \\\\ 2x\log3+5\log3=\log4 \\\\ 2x\log3=\log4-5\log3 \\\\ x\cdot2\log3=\log4-5\log3 \\\\ x=\dfrac{\log4-5\log3}{2\log3} \\\\\text{OR}\\\\ x\approx-1.8691 .\end{array}