Logarithms. Solve for m

Question

Solve $x y^m = y x^3$ for $m$.

I know this has to do with logarithms, but I'm not able to figure out how it relates to logs.

Answer 1

$xy^m=yx^3\implies \log x + m \log y=\log y + 3 \log x \implies (m-1)\log y=2\log x$

$\implies m-1=\dfrac{2\log x}{\log y}\implies m=\dfrac{2\log x}{\log y}+1$

Answer 2

Rewrite $xy^m = yx^3$ as

$$y^{m-1}=x^2$$

Take log of both sides,

$$ (m-1)\ln y = 2\ln x $$

which leads to

$$m= 2\log_y x +1$$