Logarithms-15

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Express as a single logarithm :

2 + 1 / 2 log 10 9 - 2 log 10 5

Solution:

2 + 1 / 2 log 10 9 - 2 log 10 5

= log 10 100 + 1 / 2 log 10 3 2 - log 10 5 2 [log 10 100 = 2 ; log 9 = log 3 2 and 2 log 5 = log 52]

= log 10 100 + 1 / 2 X 2 log 10 3 - log 10 25

= log 10 (100 X 3) / 25 = log 10 12 [log a + log b - log c = log { [ (a X b) / c] }

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