How do you evaluate ${ln (5^{6} \cdot 12)}^{4}$ $\ln ( 5^ { 6} \cdot 12) ^ { 4}$ ?

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Answer 1 · 2018-06-27T18:18:59

Remember $log (A \cdot B) = log A + log B$ $log(A·B)=log A+logB$ and
${log A}^{n} = n log A$ $logA^n=nlogA$

Applying log rules

${ln (5^{6} \cdot 12)}^{4} = 4 ln (5^{6} \cdot 12) = 4 ({ln 5}^{6} + ln 12) = 24 ln 5 + 4 ln 12$ $ln(5^6·12)^4=4ln(5^6·12)=4(ln5^6+ln12)=24ln5+4ln12$

How do you evaluate ln(56⋅12)4\ln ( 5^ { 6} \cdot 12) ^ { 4}?