If log 27 = 1.431 (common logarithm), find log 9.

Given data

• log 27 = 1.431 (base 10)

Concept / Approach

• Express 27 and 9 as powers of 3.
• Use log(a^k) = k log a.

Step-by-step calculation

27 = 3³ ⇒ log 27 = 3 log 3 = 1.431log 3 = 1.431 / 3 = 0.4779 = 3² ⇒ log 9 = 2 log 3 = 2 × 0.477 = 0.954

Verification

Check: log 9 + log 3 = 0.954 + 0.477 = 1.431 = log 27 which is consistent.

Common pitfalls

• Confusing base e and base 10 logs.
• Dividing 1.431 by 2 directly without first finding log 3.

Final Answer

0.954