Compute the exact value of log 8 + log(1/8) using logarithm identities.

Introduction / Context:This is a direct application of the product rule of logarithms and the defining property log(1) = 0.

Given Data / Assumptions:

• Expression: log 8 + log(1/8)
• Common base for both logs (base 10 is standard).

Concept / Approach:Use log A + log B = log(A·B). Multiplying 8 by its reciprocal gives 1, whose logarithm is zero in any base.

Step-by-Step Solution:

Verification / Alternative check:Since log(1) is 0 for any allowed base, the result is base-independent as long as the base is consistent across terms.

Why Other Options Are Wrong:1 or 2 would require the product inside the log to be 10 or 100 (base 10), which it is not. log(64) represents a different expression entirely.

Common Pitfalls:Occasionally students attempt to add arguments (8 + 1/8) rather than multiply; always add logs by multiplying their arguments.

Final Answer:0