\log _(3)(\root(3)(3)*27)/(81)
You asked:
Evaluate the expression: \(\log_{3}\left( \frac{\sqrt[3]{3} \cdot 27}{81} \right)\)
MathBot Answer:
\[\log_{3}\left( \frac{\sqrt[3]{3} \cdot 27}{81} \right) = \frac{\log{\left(\frac{\sqrt[3]{3}}{3} \right)}}{\log{\left(3 \right)}} \approx -0.66666666666666666666666666666667\]
\[\begin{aligned}\log_{3}\left( \frac{\sqrt[3]{3} \cdot 27}{81} \right)& = \log{\left(\sqrt[3]{3} \cdot \frac{27}{81} \right)}\\& = \log{\left(\sqrt[3]{3} \cdot \frac{1}{3} \right)}\\& = \log{\left(\frac{1}{3} \cdot \sqrt[3]{3} \right)}\\& = \frac{1}{\log{\left(3 \right)}} \cdot \log{\left(\frac{1}{3} \cdot \sqrt[3]{3} \right)}\end{aligned}\]