If the mantissa of log10 3274 is 0.5150, find log10 32.74.

Introduction / Context:In common logarithms, log10 N = characteristic + mantissa, where the mantissa depends only on the significant digits (order-of-magnitude independent). Moving the decimal point changes the characteristic but preserves the mantissa.

Given Data / Assumptions:

• log10 3274 has mantissa 0.5150 ⇒ log10 3274 = 3.5150.
• We need log10 32.74 (same significant digits, decimal shifted left two places).

Concept / Approach:

• Shifting decimal left by k reduces the characteristic by k.
• Mantissa remains 0.5150 (same significand 3.274 × 10^1 vs 3.274 × 10^3).

Step-by-Step Solution:

Verification / Alternative check:Direct estimation: 32.74 lies between 10 and 100, so characteristic must be 1; mantissa stays 0.5150 ⇒ 1.5150.

Why Other Options Are Wrong:

• 2.5150 would correspond to 327.4; 0.5150 would correspond to 3.274.

Common Pitfalls:

• Changing mantissa when only the decimal position changes.

Final Answer:1.5150