WAEC 2016 Mathematics · Question 9

If log2(3x - 1) = 5, find x.

Options

A.2.00
B.3.67
C.8.67
D.11

Answer: D. 11

Explanation written with AI and checked against the answer key

Analyze the question We need to find x when the logarithm (base 2) of (3x − 1) equals 5. Concept A logarithm and an exponent are inverse operations: log_b(N) = k means N = b^k Solution Step 1: Convert to index (exponential) form: 3x − 1 = 2⁵ Step 2: Evaluate the power: 2⁵ = 32, so 3x − 1 = 32 Step 3: Solve for x: 3x = 33 x = 11 Check: 3(11) − 1 = 32, and log₂(32) = 5 ✔ Answer: D (11) Tip: When you see "log_b(something) = number", immediately rewrite it as "something = b^number". Options like 3.67 and 8.67 come from common slips, such as using 2×5 = 10 instead of 2⁵ = 32 (giving 3x − 1 = 10, x = 3.67). Always remember that the power means repeated multiplication, not multiplying the base by the exponent.

AI can make mistakes. Report anything that looks wrong.