Question

How do you use the Change of Base Formula and a calculator to evaluate the logarithm `log 4^20`?

Answer 1

`log_4 20 = ln20/ln4 = log20/log4 ~~ 2.1610`

Explanation:

There is a good possibility that the intended question is to find `log_4 20` rather than the apparent question of find `log 4^20`

In any case the change of base formula says (in its general form) that

For a, b, x positive,

`log_b x = log_a x/(log_a b)`

Because calculators tend to have built-in functions for base 10 logs, `log_10` (often written `log`) and/or natural logs `ln`, it is not unusual to see the change of base formula given as:

For b, x positive,

`log_b x = log x/(log b)" "` or `" "log_b x = ln x/(ln b)`

The sequence of button to press depends on the calculator you are using.

On the calculator that is included in windows (scientific view)

press: 20 "ln" / 4 "ln" =