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 b–1) + (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)
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Go to above linked new page to download Examples, Theory and Formulas, Practice Problems and worksheets of all topics of Mathematics.