Given log 10(2) = 0.3010 and log 10(7) = 0.8451, compute log 10(2.8). Show the decomposition and calculation steps clearly.

Introduction / Context:We evaluate a common logarithm by breaking 2.8 into factors whose logs are known and using standard log identities.

Given Data / Assumptions:

• log 10(2) = 0.3010
• log 10(7) = 0.8451
• We want log 10(2.8).

Concept / Approach:Write 2.8 = 28/10 = (4×7)/10, then apply log(A/B) = log A − log B and log(AB) = log A + log B.

Step-by-Step Solution:

Verification / Alternative check:2.8 ≈ 10^0.4471 (since 10^0.4471 ≈ 2.8), confirming consistency with the computed value.

Why Other Options Are Wrong:1.4471 is log 28; 2.4471 or 14.471 are orders of magnitude too large; 0.4471 is the only value matching log 2.8.

Common Pitfalls:Forgetting to subtract 1 when converting from log 28 to log 2.8 (since 2.8 = 28/10) yields the common mistake 1.4471 instead of 0.4471.

Final Answer:0.4471