Evaluate log_9(27) − log_{27}(9).

Introduction / Context:Translate both logs to a common base (e.g., natural log) or use base–exponent recognition to evaluate each term exactly, then subtract.

Given Data / Assumptions:27 = 3^3 and 9 = 3^2.

Concept / Approach:Compute each term via ln: log_9(27) = ln 27 / ln 9 = (3 ln 3)/(2 ln 3) = 3/2. Similarly, log_{27}(9) = ln 9 / ln 27 = (2 ln 3)/(3 ln 3) = 2/3.

Step-by-Step Solution:

Final Answer:5 / 6