Evaluate log 5 (1685) to eight decimal places.

2. Hello, AFan!

You are expected to know the Base-Change Formula
. . and have a calculator.

Evaluate $\log_5(1685)$ to eight decimal places.

Base-Change Formula: . $\log_b(N) \;=\;\frac{\log(N)}{\log(b)}$ .
using any base

So we have: . $\log_5(1685) \;=\;\frac{\ln 1685}{\ln 5} \;\approx\;\boxed{4.61622085}$

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Check: . $5^{4.61622085} \:=\:1685.000009\quad\hdots$ . close enough!

3. Originally Posted by Soroban
Hello, AFan!

You are expected to know the Base-Change Formula
. . and have a calculator.

Base-Change Formula: . $\log_b(N) \;=\;\frac{\log(N)}{\log(b)}$ .
using any base

So we have: . $\log_5(1685) \;=\;\frac{\ln 1685}{\ln 5} \;\approx\;\boxed{4.61622085}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Check: . $5^{4.61622085} \:=\:1685.000009\quad\hdots$ . close enough!

How do you input that into the calculator, can anyone show me please,

$5^{4.61622085} = 1685.000009$

thanks!

4. Originally Posted by hana_102
How do you input that into the calculator, can anyone show me please,

$5^{4.61622085} = 1685.000009$

thanks!
5^4.61622085