Reciprocal of a common logarithm: Given log10 2 = 0.3010, compute log₂ 10.

Introduction / Context:
Logs with swapped base and argument are reciprocals when expressed in a common base. We use the change-of-base formula to invert log10 2.

Given Data / Assumptions:

• log10 2 = 0.3010.

Concept / Approach:
log₂ 10 = 1 / log10 2 by change of base: log₂ 10 = (ln 10)/(ln 2) and log10 2 = (ln 2)/(ln 10). Hence they are reciprocals.

Step-by-Step Solution:
log₂ 10 = 1 / 0.3010 = 1000/301 (using the given decimal as the fraction 301/1000).

Verification / Alternative check:
Numerically, 1000/301 ≈ 3.322, consistent with 10 ≈ 2^3.322.

Why Other Options Are Wrong:
0.3010 is log10 2, not its reciprocal; 0.6990 relates to log10 5; 699/301 is not the reciprocal of 301/1000.

Common Pitfalls:
Forgetting to invert; mixing up base-change direction.

Final Answer:
1000 / 301