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)