solving equation (indices/logarithms)

Question

I don't really understand the Logarithms concept when it comes to question with ln or log with base e.for example question like this:

1.solve the equation $$x^4\mathrm{e}^{-2\ln(x)}=18-3x$$

Answer 1

use the property of the logarithm: $a \log x = \log x^a$, and then the definition: $e^{\ln x} = x$