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WAEC 2022 · Paper 2 · Q13

  1. (a)

    A man and his son are 42 and 12 years old respectively. How many years ago was the product of their ages 304?

  2. (b)

    If log⁡52x+log⁡4256=1\log_5 2x + \log_4 256 = 1, find the value of xx.

Worked solution (try it first)

(a)

  1. xx years ago the man was 42−x42 - x and the son 12−x12 - x.
  2. Their product was 304: (42−x)(12−x)=304(42 - x)(12 - x) = 304, so 504−54x+x2=304504 - 54x + x^2 = 304 and x2−54x+200=0x^2 - 54x + 200 = 0.
  3. Factorise: (x−4)(x−50)=0(x - 4)(x - 50) = 0.
  4. The son is only 12, so x=50x = 50 is impossible: it was 4 years ago.
  5. Check: 38×8=30438 \times 8 = 304.

(b)

  1. log⁡4256=4\log_4 256 = 4 (since 44=2564^4 = 256), so log⁡52x=1−4=−3\log_5 2x = 1 - 4 = -3.
  2. In index form: 2x=5−3=11252x = 5^{-3} = \frac{1}{125}, so x=1250=0.004x = \frac{1}{250} = 0.004.

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