Simplifying a logarithmic equation

Question

How would one simplificate the following statement, resulting in only one log-term, if this is even possible. Thanks in advance.

$log(x)^{A}\cdot log(x)^{-\frac{1}{A-1}} - log(x)^{-\frac{1}{A-1}}$

Answer 1

I would write $$\frac{\log(x)^A-1}{\log(x)^{\frac{1}{A-1}}}$$