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4MA1/1H Jun 2021, Question 11: Exponential Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Two index equations: solve for x in √2 × 16 = 2ˣ, and for n in (11⁻⁶)⁵ ÷ 11⁴ = 11ⁿ, showing working.

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Part (a) · 2 marks

Find x where √2 × 16 equals 2ˣ, showing working.

  1. 1√2 = 2^(1/2) and 16 = 2⁴
  2. 2√2 × 16 = 2^(1/2) × 2⁴ = 2^(1/2 + 4)
  3. 31/2 + 4 = 9/2, so 2ˣ = 2^(9/2)
  4. 4x = 9/2

Answer9/2

Part (b) · 2 marks

Find n where (11⁻⁶)⁵ divided by 11⁴ equals 11ⁿ, showing working.

  1. 1(11^(−6))⁵ = 11^(−6 × 5) = 11^(−30)
  2. 2Dividing powers subtracts them: 11^(−30) / 11⁴ = 11^(−30 − 4)
  3. 3−30 − 4 = −34, so n = −34

Answer−34

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