Using the identity log(10) = 1 and 10 = 2 × 5, compute log 5 given log 2 = 0.3010.

Introduction / Context:We use basic base-10 logarithm properties and the factorization 10 = 2 × 5 to compute log 5 from a given log 2 value.

Given Data / Assumptions:

• log 2 = 0.3010
• All logs are common (base 10).

Concept / Approach:Since log(10) = 1 and 10 = 2 × 5, it follows that log 10 = log 2 + log 5. Solve for log 5 by subtraction.

Step-by-Step Solution:

Verification / Alternative check:Because 2 × 5 = 10, the result must satisfy log 2 + log 5 = 1; 0.3010 + 0.6990 = 1.0000, confirming correctness.

Why Other Options Are Wrong:0.3010 is log 2, not log 5; 0.7525 has no basis here; and it is clearly possible to compute log 5 from log 2 using the identity above.

Common Pitfalls:Forgetting that log 10 equals 1 or adding instead of subtracting when solving for log 5 can cause errors.

Final Answer:0.6990