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Which of the following is the correct change-of-base formula for logarithms?
Alog_a(x) = log_b(a) × log_b(x)
Blog_a(x) = log_b(x) + log_b(a)
Clog_a(x) = log_b(x) / log_b(a)
Dlog_a(x) = log_b(x) − log_b(a)
Answer & Solution
Correct answer: C. log_a(x) = log_b(x) / log_b(a)
1. The change-of-base law restates a logarithm in a different base.
2. log_a(x) = log_b(x) / log_b(a), valid for any b > 0, b ≠ 1.
3. It allows converting between common-log and natural-log calculations using the same identity.
_Source: ICMAI BoS CMA Foundation Paper 3 (Business Mathematics & Statistics), Module 2 §2.2 (Indices and Logarithms) + Module 5 (Standard Deviation), p. 112-160 + 318-340_