Compute log₉(81) − log₄(32). Express each exactly via prime powers and subtract.

Introduction / Context:By expressing each base and argument as a power of a common prime, we can evaluate the logarithms exactly and then subtract.

Given Data / Assumptions:

• 9 = 3^2, 81 = 3^4
• 4 = 2^2, 32 = 2^5

Concept / Approach:Use log_{p^m}(p^n) = n/m to get exact rational values.

Step-by-Step Solution:

Verification / Alternative check:Change of base to ln confirms the same rational numbers and difference.

Why Other Options Are Wrong:2 is the first term, not the difference; 1/2 has the wrong sign; −3/2 would require 2 − 3.5, which is not the case.

Common Pitfalls:Mixing up which number is base and which is argument or reversing the subtraction order changes the sign.

Final Answer:- 1 / 2