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0580/23 May/Jun 2024, Question 20: Exponential Equations

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 4 marks

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The question, in short

For f(x) = 3ˣ + 2, solve two equations: one using f(x) = 245, and one using the inverse function f⁻¹(x) = 7.

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Part (a) · 2 marks

Solve 3ˣ + 2 = 245 to find the value of x.

  1. 13ˣ + 2 = 245
  2. 23ˣ = 243 = 3⁵
  3. 3x = 5

Answer5

Part (b) · 2 marks

Given f⁻¹(x) = 7, find the value of x.

  1. 1f⁻¹(x) = 7 means x = f(7)
  2. 2x = 3⁷ + 2 = 2187 + 2 = 2189

Answer2189

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Also searched as: 0580/23/M/J/24 · 0580_s24_qp_23 · 0580 s24 23 · question 20.
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