If log 27 = 1.431, then the value of log 9 is:

Concept: The power rule of logarithms states log(an) = n × log(a) — the exponent on the argument becomes a multiplying factor in front of the logarithm.

Application:

1. 27 = 33, so log 27 = 3 × log 3.

2. Given log 27 = 1.431, log 3 = 1.431 ÷ 3 = 0.477.

3. 9 = 32, so log 9 = 2 × log 3.

4. Substituting log 3 = 0.477: log 9 = 2 × 0.477 = 0.954.

Cross-check: 9 = 27(2/3), so log 9 = (2/3) × log 27 = (2/3) × 1.431 = 0.954 — the same result by an independent route, confirming the answer.