If log₁₀ 2 = a and log₁₀ 3 = b, then express log₅ 12 in terms of a and b.

Model Answer & Options

Source: Extra Practice

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

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

(2a + b) / a

(a + b) / (1 - a)

Explanation

Using change of base: log₅ 12 = log₁₀ 12 / log₁₀ 5. Numerator: log₁₀ 12 = log₁₀(2² * 3) = 2log₁₀ 2 + log₁₀ 3 = 2a + b. Denominator: log₁₀ 5 = log₁₀(10/2) = log₁₀ 10 - log₁₀ 2 = 1 - a. Thus, log₅ 12 = (2a + b) / (1 - a). Option A is correct.

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