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Use the property of logarithm to expand and simplify the expression ?

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asked Jun 27, 2023 20.9k views

1 vote

Use the property of logarithm to expand and simplify the expression ?

Mathematics
high-school

Bjarven asked

by Bjarven

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1 Answer

7 votes

Simplify expression

$\begin{gathered} \log _(12)\sqrt[3]{(12+x)/(144x)}= \\ =\log _(12)((12+x)/(144x))^{(1)/(3)}= \\ =(1)/(3)\log _(12)((12+x)/(144x))= \\ =(1)/(3)(\log _(12)(12+x)-\log _(12)(144x))= \\ =(1)/(3)(\log _(12)(12+x)-(\log _(12)(144)+\log _(12)(x)))= \\ =(1)/(3)(\log _(12)(12+x)-2+\log _(12)(x))= \\ =(1)/(3)\log _(12)(12+x)-(2)/(3)+(1)/(3)\log _(12)x \end{gathered}$

So our final answer will be: