Simplify natural logarithm when there is a constant

Question

Apologies for lack of latex.

I am trying to simplify ln(x^2)+1 / ln(x)

ln(x^2) + 1  / ln(x)
= 2 * (ln(x)) + 1 / ln(x)
= 2 + (1 / ln(x))

I understand we can get 2 ln(x) from ln(x^2). How did we get from step 2 to step 3?

Answer 1

There are parenthesis missing. It should be\begin{align}\frac{\ln(x^2)+1}{\ln x}&=\frac{2\ln(x)+1}{\ln x}\\&=\frac{2\ln x}{\ln x}+\frac1{\ln x}\\&=2+\frac1{\ln x}.\end{align}