Question

show that log 360 =3 log 2+ 2 log 3 + log 5

Answer 1

Hi...☺

Here is your answer...✌
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$log(360) = log(36 \times 10) \\ \\ = log( 36 ) + log(10) \\ \\ = log( {6}^{2} ) + log(2 \times 5) \\ \\ = 2 log(6) + log(2) + log(5) \\ \\ = 2 log(3 \times2 ) + log(2) + log(5) \\ \\ = 2( log(3) + log(2) ) + log(2) + log(5) \\ \\ = 2 log(3) + 2 log(2) + log(2) + log(5) \\ \\ = 3 log(2) + 2 log(3) + log(5)$