Answer: \(x=\frac16\).

Answer: \(x=\frac16\).

Use the logarithm law \(\log a-\log b=\log\left(\frac{a}{b}\right)\):

\(\log_5\left(\frac{8x+7}{2x}\right)=2.\)

Since \(2=\log_5 25\),

\(\frac{8x+7}{2x}=25.\)

Therefore

\(8x+7=50x,\)

so \(42x=7\), giving

\(x=\frac16.\)