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TMUA 2018 · Paper 1 · Question 14 of 20

TMUA 2018 Paper 1 Question 14

Exponentials and logarithms — Logarithms · a line through two related points. Try it first; the answer and a full worked solution are below.

TMUA 2018 · Paper 1Exponentials and logarithmsLogarithms · a line through two related points6 options
The line y = mx + 4 passes through the points (3,  log2 p) and (log2 p,  4).

What are the possible values of p?

  1. Ap = 1 and p = 4
  2. Bp = 1 and p = 16
  3. Cp = 14 and p = 4
  4. Dp = 14 and p = 64
  5. Ep = 164 and p = 4
  6. Fp = 164 and p = 16
Show the answer and worked solution
answer · B
  1. Ap = 1 and p = 4
  2. Bp = 1 and p = 16
  3. Cp = 14 and p = 4
  4. Dp = 14 and p = 64
  5. Ep = 164 and p = 4
  6. Fp = 164 and p = 16
Put t = log2 p. The second point gives 4 = mt + 4, so mt = 0: either t = 0 or m = 0. If t = 0 then p = 1, and the first point (3,  0) forces 0 = 3m + 4, so m = −43, which is consistent. If instead m = 0 the line is y = 4, so the first point gives t = 4 and p = 16. The possible values are p = 1 and p = 16.