Suppose someone said to you:
$$\forall x \in \mathbb{Z}^+, log((-x)^2) = 2 \cdot log(-x)$$
Is this statement correct or incorrect to make since x is in $\mathbb{N}$? Should it be stated as equal to: $2 \cdot log(x)$? Is there any possible way the above equation could be incorrect? Or is it 100% valid?
The logarithm of a negative number is not defined in $\mathbb{R}$. So, the correct formula, is $$ \log (x^2)=2\log|x| $$ Thai is valid for positive or negative $x$ ($x\ne0$)