# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_3 48?

Jan 12, 2016

≈ 3.524 (3 decimal places)

#### Explanation:

${\log}_{a} x$ may be converted to the base b by using the following formula :

${\log}_{b} \frac{x}{\log} _ b a$ (x > 1 )

In this case write ${\log}_{3} 48 = {\log}_{10} \frac{48}{\log} _ 10 3$

Other bases , apart from base 10 may be used. Base 10 is convenient as it can be evaluated on a calculator ( as of course can ln)

When using base 10 it is usual for it to be written without the 10.

$\Rightarrow {\log}_{10} \frac{48}{\log} _ 10 3 = \log \frac{48}{\log} 3$

using the log key on a calculator (this is to base 10 )

rArr log48/log3 = 1.68124/0.47712 ≈3.524