Evaluate log 5 (1685) to eight decimal places.
Hello, AFan!
You are expected to know the Base-Change Formula
. . and have a calculator.
Evaluate $\displaystyle \log_5(1685)$ to eight decimal places.
Base-Change Formula: .$\displaystyle \log_b(N) \;=\;\frac{\log(N)}{\log(b)}$ . using any base
So we have: .$\displaystyle \log_5(1685) \;=\;\frac{\ln 1685}{\ln 5} \;\approx\;\boxed{4.61622085}$
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Check: .$\displaystyle 5^{4.61622085} \:=\:1685.000009\quad\hdots$ . close enough!