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

ajanlr 2022-10-17 Answered
Logarithm doubt ...
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 l o g of 5 square is possible ....can anyone explain this? Thanks
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Answers (1)

Taxinov
Answered 2022-10-18 Author has 18 answers
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.)
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