log7(7^5/6)

asked by guest
on Nov 25, 2024 at 3:17 am



You asked:

Evaluate the expression: log⁡7(756)\log_{7}\left( \frac{{7}^{5}}{6} \right)

MathBot Answer:

log⁡7(756)=−log⁡(6)log⁡(7)+5≈4.0792177788383982096812727548238\log_{7}\left( \frac{{7}^{5}}{6} \right) = - \frac{\log{\left(6 \right)}}{\log{\left(7 \right)}} + 5 \approx 4.0792177788383982096812727548238

log⁡7(756)=log⁡(75⋅16)=log⁡(168076)=5−1log⁡(7)⋅log⁡(6)\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}

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