The value of the expression 1/(1 + log_a(bc)) + 1/(1 + log_b(ca)) + 1/(1 + log_c(ab)) is _______ A. -1 B. 0 C. 1 D. 3

GATE 2018 · General Aptitude · Logarithms · medium

Answer: The expression equals 1. Answer: C. 1

1. Simplify each denominator: Similarly: 1 + log_b(ca) = log_b(abc) and 1 + log_c(ab) = log_c(abc). The expression becomes 1/log_a(abc) + 1/log_b(abc) + 1/log_c(abc).
2. Apply reciprocal of log as change-of-base: The expression becomes log_{abc}(a) + log_{abc}(b) + log_{abc}(c).
3. Sum the logarithms: log_{abc}(abc) = 1, since any logarithm of its own base equals 1.