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

Logarithm doubt ...
I know that log of a negative number is not possible but, $\mathrm{log}\left(-5{\right)}^{2}$ is possible. Therefore $\mathrm{log}\left(-5{\right)}^{2}=2\mathrm{log}\left(-5\right)$ but $\mathrm{log}\left(-5\right)$ is not possible but $log$ of $-5$ square is possible ....can anyone explain this? Thanks
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Taxinov
There is no reason to expect that
$\mathrm{log}{a}^{b}=b\mathrm{log}a$
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.)