Evaluate the logarithmic expression: log_2(32) - log_3(81) + ln(e^5).

Answer and explanation

Correct answer: A. 6

  1. Step 1: Evaluate each logarithm individually:
  2. Step 2: log_2(32) = 5 (since 2^5 = 32);
  3. Step 3: log_3(81) = 4 (since 3^4 = 81);
  4. Step 4: ln(e^5) = 5 (by inverse property).
  5. Step 5: Combine terms: 5 - 4 + 5 = 1 + 5 = 6.
Answer
6.
Why not the others: '4' subtracts 5 from 5 and leaves 4; '5' ignores log_3(81); '8' adds all terms without subtracting 4.

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