Logarithm doubt ...

Question

I know that log of a negative number is not possible but, $\log(-5)^2$ is possible. Therefore $\log(-5)^2=2\log(-5)$ but $\log(-5)$ is not possible but $log$ of $-5$ square is possible ....can anyone explain this? Thanks

Answer 1

There is no reason to expect that $$ \log a^b = b\log a $$ holds for $a<0$.

(Once you get to complex logarithms, you can make sense of such equalities, but only if you allow multi-valued interpretations of the logarithm.)