By the product rule, log(M · N) = log(M) + log(N). Since 4 × 3 = 12, log(4) + log(3) = log(12). Option A has no logarithm rule for products of logs (that would give log(2^log(6)), not log(12)). Option C gives log(32) and option D gives log(20).
Question 2 True / False
log(M + N) = log(M) + log(N) for any positive M and N.
TTrue
FFalse
Answer: False
The product rule says log(M · N) = log(M) + log(N) — it applies to the log of a product, not a sum. There is no simplification rule for log(M + N). For example, log(10 + 10) = log(20) ≈ 1.30, but log(10) + log(10) = 1 + 1 = 2. Confusing addition inside the log with addition outside the log is the most common logarithm error.
Question 3 Short Answer
Use the power rule to explain step-by-step why log₂(8) = 3.
Think about your answer, then reveal below.
Model answer: 8 = 2³, so log₂(8) = log₂(2³) = 3 · log₂(2) = 3 · 1 = 3
The power rule states log_b(M^p) = p · log_b(M). Recognizing that 8 = 2³ lets you rewrite the argument as a power of the base, then pull the exponent out front. Since log_b(b) = 1 always, log₂(2) = 1, so the result is 3 · 1 = 3. This shows the power rule is consistent with the definition of logarithm.