WAEC 2018 Mathematics · Question 14
If (6x - 4) - 2 = 1, solve for x.
Options
- A.2
- B.3
- C.4
- D.5
Answer: C. 4
Explanation written with AI and checked against the answer key
Analyze the question: We have a logarithmic equation with a difference of two logs, and we need to find x. Concept: The quotient rule for logarithms says log a − log b = log(a/b). Also, log₁₀ 10 = 1, so 1 = log₁₀ 10. Solution: Step 1: Combine the logs. log₁₀[(6x − 4)/2] = 1 Step 2: Convert to index (exponential) form. (6x − 4)/2 = 10¹ = 10 Step 3: Solve for x. 6x − 4 = 20 6x = 24 x = 4 Check: log₁₀(6(4) − 4) − log₁₀ 2 = log₁₀ 20 − log₁₀ 2 = log₁₀ 10 = 1 ✓ The argument 6x − 4 = 20 is positive, so the solution is valid. Tip: When you see a log equal to a number, rewrite the number as a log of the base (here 1 = log₁₀ 10), or convert directly to index form. Always check that the value inside the log is positive.AI can make mistakes. Report anything that looks wrong.
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