# How do you calculate log_6 83 with a calculator?

Aug 16, 2016

See explanation.

#### Explanation:

Usually calculators have decimal logarythm $\log$ and natural logarythm $\ln$. To calculate logarythm of a different base you can use the Base Change formula:

## ${\log}_{c} x = {\log}_{b} \frac{x}{\log} _ b c$

In the given example to calculate ${\log}_{6} 83$ you can use the formula:

${\log}_{6} 83 = \log \frac{83}{\log} 6$

To calculate the value you do the following:

1. Press $6$ and $\log$ to calculate $\log 6$.
2. Put the result in memory.
3. Press $83$, $\log$,$\div$
4. Recall result calculated in 1. from memory
5. Press $=$ to calculate the result.

Note: I used the decimal logarythm. You can also use natural logarythm in the procedure.