Find all vertical and horizontal asymptotes of

f(x) = ln(2x)/ln(x^2)

I understand for vertical asymptote, there is one at x = 1, because denominator becomes 0.

But for horizontal asymptote, i know as x -> inf, the denominator will increase faster than the numerator because of the squared, but is there a way to show it mathematically?

Like with polynomials, you divide by the highest power, but with ln, what do you do?

Thanks.