Answer
$x=\dfrac{\log3+2\log8}{4\log8}\\\\
x\approx0.6321
$
Work Step by Step
Getting the logarithm of both sides and then using the properties of logarithms, the value of $x$ in the expression $
8^{4x-2}=3
$ is
\begin{array}{l}
\log8^{4x-2}=\log3\\\\
(4x-2)\log8=\log3\\\\
4x\log8-2\log8=\log3\\\\
4x\log8=\log3+2\log8\\\\
x=\dfrac{\log3+2\log8}{4\log8}\\\\
x\approx0.6321
.\end{array}
