Answer
$x=\dfrac{\log4+5\log5}{3\log5}\\\\
x\approx1.9538
$
Work Step by Step
Getting the logarithm of both sides and then using the properties of logarithms, the value of $x$ in the expression $
5^{3x-5}=4
$ is
\begin{array}{l}
\log5^{3x-5}=\log4\\\\
(3x-5)\log5=\log4\\\\
3x\log5-5\log5=\log4\\\\
3x\log5=\log4+5\log5\\\\
x=\dfrac{\log4+5\log5}{3\log5}\\\\
x\approx1.9538
.\end{array}
