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Question

Express each of the following as a single logarithm: 12log36+2log8-log1.5.


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Solution

Simplify the expression.

Given expression is 12log36+2log8-log1.5

12log36+2log8-log1.5=12log62+2log23-log1510=log6+6log2-log1510[logan=nloga]=log2×3+6log2-log32=log2+log3+6log2-log3+log2[logab=loga+logb,logab=loga-logb]=8log2

Hence, the required single logarithm is 8log(2).


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