Solving $(-\log x)^2$

Question

I find this property of logarithms quite confusing.

$$(-\log x)^2 = (\log x)^2$$

Can also be

$$(-\log x)^2 = \Big(\log \big(\tfrac{1}{x}\big)\Big)^2$$

Which one is correct?

Answer 1

Both are correct.

The first one is not a property of logarithms, it's a property of squares. (-a)²=a² for all a.

The second one follows from the first because log(1/x) = log(x⁻¹) = -log(x)