WAEC 2014 Mathematics · Question 28

If 23x = 325, find the value of x

Options

Answer: A. 7

Explanation written with AI and checked against the answer key

The question is probably meant to be 2₃x = 325 in some base, but as typed it can be read in a few ways. Let's check them. Reading 1: 23ₓ = 325 (the number 23 in base x equals 325) 23ₓ = 2x + 3. Setting 2x + 3 = 325 gives x = 161, which is not among the options. Reading 2: 23 in base x equals 25 in base something This doesn't fit the options either. Reading 3: 23ₓ = 325 where 325 is in base 10 and 23 is in base x This is the same as Reading 1, so no match. Reading 4: the original WASSCE question, 23ₓ = 32₅ (the "5" is the base subscript) This is the standard version of the question: 23ₓ = 32₅, and it fits the options. Step 1: Convert 32₅ to base 10 32₅ = 3×5 + 2 = 17 Step 2: Express 23ₓ in base 10 23ₓ = 2×x + 3 = 2x + 3 Step 3: Equate and solve 2x + 3 = 17 2x = 14 x = 7 Check: 23 in base 7 = 2×7 + 3 = 17, and 32 in base 5 = 3×5 + 2 = 17 ✓. Also, the digit 3 must be smaller than the base, and 7 > 3, so it is valid. Answer: A (7) I should say that, written literally as "325" in base 10, the equation gives 161, which isn't an option. Exam tip: For base-conversion questions, convert both sides to base 10 first, then solve the simple equation. Always check that each digit is smaller than its base.

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