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0580/21 Oct/Nov 2021, Question 22: Exponential Equations

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 5 marks

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The question, in short

Simplify an index fraction, find k from 16 = 64ᵏ, and solve an equation in x involving powers of 3 and 1/9.

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

Part (a) · 1 mark

Simplify the quotient of x to the power 2/3 divided by x to the power 8/3.

  1. 1x^(2/3 − 8/3) = x⁻²
  2. 2= 1/x²

Answerx⁻² or 1/x²

Part (b) · 1 mark

Find the value of k that satisfies 16 = 64ᵏ.

  1. 116 = 4² and 64 = 4³, so 4² = 4³ᵏ
  2. 23k = 2, k = 2/3

Answer2/3

Part (c) · 3 marks

Solve 3³ˣ × (1/9)⁴⁻³ˣ = 3 for x.

  1. 11/9 = 3⁻², so (1/9)⁴⁻³ˣ = 3⁻²⁽⁴⁻³ˣ⁾
  2. 23³ˣ × 3⁻⁸⁺⁶ˣ = 3¹
  3. 33x − 8 + 6x = 1
  4. 49x = 9, x = 1

Answer1

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Also searched as: 0580/21/O/N/21 · 0580_w21_qp_21 · 0580 w21 21 · question 22.
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