Answer: \(x=\dfrac{e^{1/3}}5\) or \(x=\dfrac1{5e}\).

The key point is to rewrite the equation using logarithm laws or a suitable substitution.

Let \(u=\ln(5x)\). Then the equation becomes

\(3u^2+2u-1=0.\)

Factorising,

\((3u-1)(u+1)=0.\)

Hence

\(u=\frac13\quad\text{or}\quad u=-1.\)

Therefore

So

\(5x=e^{1/3}\quad\text{or}\quad 5x=e^{-1}.\)

Thus