# Examples on Logarithms

## EXAMPLES ON LOGARITHMS Here are some examples on logarithms very important for High school Mathematics

Examples
Example 1:

If loga3 = 2 and logb 8 = 3, then loga b is
(a)  log3 2                     (b)  log2 3                     (c)  log3 4                     (d)  log4 3
Solution:
logb8 = 3   Þ  3 logb2 = 3   Þ  logb2 = 1    Þ  b = 2
logab = log2 b . loga 2
= log2 b . log3 2 . loga3 = 1 . (log3 2) . 2 = 2 log3 2 = log3 4
(c)
Example 2:
If a, b, c are distinct positive numbers different from 1 such that
(logba . logca logaa) + (logab. logcb logbb) + (logac. logbc logc c) = 0, then abc=
(a)  0                            (b)  e                            (c)  1                            (d)  none of these
Solution :
(logb a logc a 1) + (loga b . logc b1) + (loga c logbc 1) = 0
Þ   \$frac{log a}{log b} . frac{log a}{log c}+frac{log b}{log a} . frac{log b}{log c}+frac{log b}{log a} . frac{log c}{log b}=3\$
Þ   (log a)3 + (log b)3 + (log c)3 = 3log a log b log c
Þ   (log a + log b + log c) = 0              [Q If a3 + b3 + c3 3abc = 0 then a + b + c = 0 if a ¹ b¹c]
Þ   log abc = log 0        Þ   abc= 1
(c)