If log 10(2) = 0.301, evaluate log 10(50). Show your factorization and calculation.

Introduction / Context:This question checks basic fluency with common-log rules and factorization of 50 into convenient components.

Given Data / Assumptions:

• log 10(2) = 0.301
• We seek log 10(50).

Concept / Approach:Use 50 = 5 × 10 and log(AB) = log A + log B. Also use log 5 = 1 − log 2 because 10 = 2 × 5.

Step-by-Step Solution:

Verification / Alternative check:Because 50 is 5 × 10, we expect log 50 to be slightly less than log 100 = 2; indeed, 1.699 fits this expectation.

Why Other Options Are Wrong:1.301 would be log(20); 2.301 is log(200); 0.699 is log 5, not log 50.

Common Pitfalls:Using log 5 = log 10 − log 2 is correct; mixing the sign or adding instead of subtracting will produce the wrong intermediate value.

Final Answer:1.699