Without using a calculator, evaluate \(\frac{{{\left( {{\log }_{4}}9 \right)}^{2}}\times {{\log }_{9

Question

Without using a calculator, evaluate $\frac{{{\left( {{\log }_{4}}9 \right)}^{2}}\times {{\log }_{9}}16}{{{\log }_{\frac{1}{5}}}5\times \ln 81}$, leaving the answer in terms of $\ln 2$.

Accepted Answer

$-\displaystyle\frac{1}{2\ln 2}$

Exponential and Logarithmic Functions - Laws of Logarithms

Exponential and Logarithmic Functions - Laws of Logarithms

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