Question

Simplify:
log 81/8 + 2log 2/3 -3 log 3/2 + log 3/4

Answer 1

Question :-

Simplify it .

$\sf log( \frac{81}{8} ) + 2 log( \frac{2}{3} ) - 3 log( \frac{3}{2} ) + log( \frac{3}{4} )$

Answer :-

→ 0

Formula used :-

$\star \sf \: log( \frac{m}{n} ) = log(m) - log(n) \\ \\ \star \: \sf log( {m}^{n} ) = n log(m)$

Explanation:-

We have ,

$\rightarrow \: \sf log( \frac{81}{8} ) + 2 log( \frac{2}{3} ) - 3 log( \frac{3}{2} ) + log( \frac{3}{4} ) \\ \: \\ \rightarrow \sf log(81) - log(8) + 2 log(2) - 2 log(3) \\ \: \: \: \: \sf - 3 log(3) + 3 log(2) + log(3) - log(4) \\ \\ \rightarrow \sf log( {3}^{4} ) - log( {2}^{3} ) + 2 log(2) - 2 log(3) \\ \: \ \: \sf- 3 log(3) + 3 log(2) + log(3) - log( {2}^{2} ) \\ \\ \rightarrow \sf 4 log(3)- 3 log(2) + 2 log(2)- 2 log(3) \\ \: \: \sf- 3 log(3) + 3 log(2) + log(3) - 2 log(2) \\ \\ \bf \: now \: arrange \: these \\ \\ \rightarrow \sf 4 log(3) - 2 log(3) - 3 log(3) + log(3) \\ \: \: \sf - 3 log(2) + 2 log(2) + 3 log(2) - 2 log(2) \\ \\ \rightarrow \sf4 log(3) - 4 log(3) - 5 log(2) + 5 log(2) \\ \\ \rightarrow \: 0$

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