# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_4 24?

Jun 12, 2018

Below

#### Explanation:

The change of base formula is given by: ${\log}_{a} b = {\log}_{10} \frac{b}{\log} _ 10 a$

Looking at ${\log}_{4} 24$, we can tell that a=4 and b=24.

${\log}_{4} 24 = {\log}_{10} \frac{24}{\log} _ 10 4 = 2.292$

Jun 12, 2018

$y = 2.29248$(5 dps)

#### Explanation:

from first principles

$y = {\log}_{4} 24$

$\implies {4}^{y} = 24$

take logs to both sides ( we will use base 10)

$\log {4}^{y} = \log 24$

$y \log 4 = \log 24$

$y = \log \frac{24}{\log} 4$

$y = 2.29248125$

note: some calculators now have a function that can evaluates logarithms in any base