Evaluate the expression using common-base logarithm rules: log(9/8) − log(27/32) + log(3/4). Simplify by combining as a single logarithm and compute its value.

Introduction / Context:
We simplify an expression with base-10 logarithms (any common base works since the base is consistent) by using product and quotient properties to combine terms, then evaluate.

Given Data / Assumptions:

• Expression: log(9/8) − log(27/32) + log(3/4)
• All logs are in the same base (common logarithms).

Concept / Approach:
Use log A − log B = log(A/B) and log A + log B = log(A·B). Combine the three terms into one logarithm and then simplify the numeric fraction inside.

Step-by-Step Solution:

Verification / Alternative check:
Note that (9/8)*(3/4) = 27/32 exactly. Hence log(9/8) + log(3/4) = log(27/32), so subtracting log(27/32) yields 0, which equals log(1).

Why Other Options Are Wrong:
1, 2, and 3 correspond to log values of 10, 100, 1000 respectively; the combined argument equals 1, not a power of 10 other than 10^0. “None of these” is unnecessary since 0 is available and correct.

Common Pitfalls:
Mixing the order of operations or incorrectly adding/subtracting logs without first converting to a single argument causes errors. Always convert sums/differences of logs to a product/quotient inside a single log before evaluation.

Final Answer:
0