Answer
{$\frac{1}{4}(\frac{\log 3}{\log 8}+2)$}, {$0.6321$}
Work Step by Step
Step 1: $8^{4x-2}=3$
Step 2: $\log 8^{4x-2}=\log 3$
Step 3: $(4x-2)\log 8=\log 3$
Step 4: $(4x-2)=\frac{\log 3}{\log 8}$
Step 5: $4x=\frac{\log 3}{\log 8}+2$
Step 6: $x=\frac{1}{4}(\frac{\log 3}{\log 8}+2)\approx0.6321$
Therefore, the exact solution is {$\frac{1}{4}(\frac{\log 3}{\log 8}+2)$} whereas the four decimal approximation is {$0.6321$}.
