Evaluate: log(a^2 / (b c)) + log(b^2 / (a c)) + log(c^2 / (a b)). Simplify to a single constant value.

Introduction / Context:We simplify a sum of logarithms involving symmetric rational expressions in a, b, and c. The task is purely algebraic, requiring log combination rules.

Given Data / Assumptions:

• Expression: log(a^2/(bc)) + log(b^2/(ac)) + log(c^2/(ab))
• a, b, c > 0 (so logs are defined).

Concept / Approach:Use log A + log B + log C = log(ABC). Multiply the three rational expressions and simplify the resulting fraction by collecting powers of a, b, c in numerator and denominator.

Step-by-Step Solution:

Verification / Alternative check:By exponent rules: exponents of a, b, and c in the product are 2 − 1 − 1 = 0 each, confirming that every variable cancels and the product is 1.

Why Other Options Are Wrong:1 would equal log(10) in base 10, not log(1); abc or ab2c2 are not constants and do not reflect the cancellation evident above.

Common Pitfalls:Forgetting to add exponents in the denominator or mishandling cancellations can obscure that the product equals 1 and the log is 0.

Final Answer:0