# Change of Base of Logarithms

### Change of Base of Logarithms

${\log _a}b = \frac{{{{\log }_c}b}}{{{{\log }_c}a}}$
and
${\log _a}b = \frac{1}{{{{\log }_b}a}}$
Example:
Find the value of the following:
a. $${\log _{25}}100$$
b. $${\log _3}0.45$$
$log 25 100 = log 10 100 log 10 25 = 10 1.3979 =7.154$ b.
$log 3 0.45 = log 10 0.45 log 10 3 = −0.3468 0.4771 =−0.727$