Examples on Logarithms

EXAMPLES ON LOGARITHMS

examples on logarithms, IIT JEE Main Advanced, competitive exams, CBSE, SAT, IGCSE, ICSE and High school Mathematics

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)
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