Logarithm-11

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If log10 2 = a; log10 3 = b, what is the value of log5 12?

Solution: log5 12 = log10 12 / log10 5

= log10 12 / log10 (10 / 2) = log10 12 / [log10 10 - log10 2]

= [log10 (22 X 3)] / [1 - log10 2] = [2 X log10 2 + log10 3] / [1 - log10 2]

= (2a + b) / (1 - a)

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