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

Aug 15, 2015

${\log}_{4} 20 = \ln \frac{20}{\ln} 4 = \log \frac{20}{\log} 4 \approx 2.1610$

#### 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,

${\log}_{b} x = {\log}_{a} \frac{x}{{\log}_{a} b}$

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,

${\log}_{b} x = \log \frac{x}{\log b} \text{ }$ or $\text{ } {\log}_{b} x = \ln \frac{x}{\ln b}$

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" =