Question

How do you use the Change of Base Formula and a calculator to evaluate the logarithm `log_3 73`?

Answer 1

`log_3 73~~3.095`

Explanation:

The Change of Base Formula says that:

`log_a x=log_b x/log_b a`

Calculators don't have `log_3 x` button, but they have "log" which is base 10 logarythm and "ln" which is natural logarythm (base `e`), so you can use this formula in such a way (using base 10 log):

1) Calculate `log 3`
2) Put the result in memory (button "X->M" or simmilar)
3) Calculate `log 73`
4) Press divide button
5) Recall memory result (button "RM" or simmilar)
6) Press result (=) button.

Note: Using "ln" instead of "log" is also possible.