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. \({\log _3}0.45\)
Answer:
a.
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