\log 3\sqrt{8}\div \log 2^4
You asked:
Evaluate the expression: \(\log\left( \frac{3 \cdot \sqrt{8}}{\log\left( {2}^{4} \right)} \right)\)
MathBot Answer:
\[\log\left( \frac{3 \cdot \sqrt{8}}{\log\left( {2}^{4} \right)} \right) = \log{\left(\frac{6 \sqrt{2}}{\log{\left(16 \right)}} \right)} \approx 1.11855161896980136369906833442611\]
\[\begin{aligned}\log\left( \frac{3 \cdot \sqrt{8}}{\log\left( {2}^{4} \right)} \right)& = \log{\left(3 \cdot \sqrt{8} \cdot \frac{1}{\log{\left(2^{4} \right)}} \right)}\\& = \log{\left(3 \cdot 2 \cdot \sqrt{2} \cdot \frac{1}{\log{\left(2^{4} \right)}} \right)}\\& = \log{\left(3 \cdot 2 \cdot \sqrt{2} \cdot \frac{1}{\log{\left(16 \right)}} \right)}\\& = \log{\left(6 \cdot \sqrt{2} \cdot \frac{1}{\log{\left(16 \right)}} \right)}\end{aligned}\]