Question

4. (a) Evaluate : 3log2 - log 27 + log 12 - log 4 + 3log 5
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Answer 1

Step-by-step explanation:

$\green{ \large\rightarrow{ \sf \: GIVEN} \leftarrow}$

$\displaystyle\sf \: 3 log(2) - log(27) + log(12) - log(4) + 3 log(5)$

$\green{ \large\rightarrow{ \sf \:SOLUTION} \leftarrow}$

$\displaystyle\sf \: 3 log(2) - log(27) + log(12) - log(4) + 3 log(5) \\ \\ \sf = log( {2}^{3} ) - log(27) + log(12) - log(4) + log( {5}^{3} ) \\ \\ \sf \: = \{ log(8) + log(12) + log(125) \} - \{ log(27) + log(4) \} \\ \\ = \sf \: log(8 \times 12 \times 125) - log(27 \times 4) \\ \\ \sf \: = log ( \frac{8 \times 12 \times 125}{27 \times 4} ) \: \: \: \: \: \: \: \: \\ \\ = \sf \: log ( \frac{8 \times \cancel{12} {}^{ \: \: \: \: \cancel3} \times 125}{ \cancel{27} {}^{ \: \: \: \: 9} \times \cancel4} ) \\ \\ \sf \:= log( \frac{1000}{9} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf \: Required \: Ans = log( \frac{1000}{9} )$