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WMA12/01 Jan 2020, Question 9: Solving Exponential and Log Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Sketch y = 3 × 4ˣ giving axis intercept coordinates, then show the x coordinate where y = 6¹⁻ˣ meets it equals log₁₀ 2 ÷ log₁₀ 24.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Sketch the curve y = 3 × 4ˣ, marking the coordinates of any intersections with the coordinate axes.

  1. 1When x = 0, y = 3 × 4⁰ = 3, so the curve meets the y-axis at (0, 3)
  2. 23 × 4ˣ > 0 for all x, so the curve never meets the x-axis
  3. 3As x → −∞, y → 0 (asymptote y = 0); as x increases, y increases rapidly

AnswerIncreasing exponential curve, always above the x-axis, with the negative x-axis as an asymptote (y → 0 as x → −∞), crossing the y-axis at (0, 3); no x-intercept

Part (b) · 5 marks

Show that the x coordinate of the meeting point P of y = 6¹⁻ˣ and y = 3 × 4ˣ is log₁₀ 2 ÷ log₁₀ 24.

  1. 16¹⁻ˣ = 3 × 4ˣ
  2. 2Take logs: (1 − x) log 6 = log 3 + x log 4
  3. 3log 6 − log 3 = x log 4 + x log 6
  4. 4x log 24 = log 2
  5. 5x = log₁₀ 2 / log₁₀ 24

AnswerShown: x(log 4 + log 6) = log 6 − log 3 ⇒ x = log 2 / log 24

Stuck on a step? Read the free lesson: Solving Exponential and Log Equations

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