Question

Describe when the change of base formula could come in handy.

Answer 1

Step 1

In order to evaluate logarithms with a base other than 10, we use the change-of-base formula to rewrite the logarithm as the quotient of logarithms of any other base; when using a calculator, we would change them to common or natural logs.

So if for instance we are given;

`log_35`

The logarithm above is in base 3 and not 10. The change of base formula will now come in and we rewrite the logarithm as the quotient of logarithms of any other base e.g base 10 or natural logs. So we can write;

`log_35=(log_(10)5)/(log_(10)3)`