NECO 2024 · Paper 1 · Q13

Solve 23x=16342^{3x} = 16^{\frac34}.

Worked solution (try it first)
  1. Write 16 as 242^4: 1634=(24)34=2316^{\frac34} = (2^4)^{\frac34} = 2^3, multiplying the indices.
  2. So 23x=232^{3x} = 2^3, and the powers are equal: 3x=33x = 3.
  3. Divide by 3: x=1x = 1, option E.

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