How to find power scaling of expressi0n containing ln?

Question

$y(x)=\frac{1}{\ln({\frac{a*x}{-\ln(1-b/x^2)}})}$

Can we tell what is the scaling behavior of $y(x)$ goes as $x^{(some-power)}$

$b/x^2$ is small

Answer 1

If $\frac b{x^2} \ll 1, -\ln(1-\frac b{x^2}) \approx \frac b{x^2}$ If you plug this in, you still won't get polynomial behavior for $y(x)$ because of the other $\ln$