log7(7^5/6)
You asked:
Evaluate the expression: \(\log_{7}\left( \frac{{7}^{5}}{6} \right)\)
MathBot Answer:
\[\log_{7}\left( \frac{{7}^{5}}{6} \right) = - \frac{\log{\left(6 \right)}}{\log{\left(7 \right)}} + 5 \approx 4.0792177788383982096812727548238\]
\[\begin{aligned}\log_{7}\left( \frac{{7}^{5}}{6} \right)& = \log{\left(7^{5} \cdot \frac{1}{6} \right)}\\& = \log{\left(\frac{16807}{6} \right)}\\& = 5 - \frac{1}{\log{\left(7 \right)}} \cdot \log{\left(6 \right)}\end{aligned}\]