Question

How do you use the Change of Base Formula and a calculator to evaluate the logarithm `log_3 40`?

Answer 1

You divide `log(40)` by `log(3)` or divide `ln(40)` by `ln(3)`

Explanation:

Change of base means that you divide the log (to the new base) of the number by the log (to the new base) of the old base.

You may use `log=log_10` or the `ln=log_e` as long as you use the same button both times.

So:
`log_3 40=log40/log3=(1.6020...)/(0.4771...)=3.3577...`
Or:
`log_3 40=ln40/ln3=(3.6888...)/(1.0986...)=3.3577...`

Of course you can do this in one go, as long as you mind the brackets.