Logarithms-14

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Express log 10 108 1 / 5 in terms of log 10 2 and log 10 3.

Solution:

log 10 108 1 / 5 = 1 / 5 log 10 108 [log 10 n m = m log 10 n]

= 1 / 5 log 10 (2 2 X 3 3) [ 108 = 2 X 2 X 3 X 3 X 3 = 2 2 X 3 3 ]

= 1 / 5 [log 10 2 2+ log 10 3 3] [log 10 (m X n) = log 10 m + log 10 n]

= 1 / 5 [2 log 10 2 + 3 log 10 3]

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