0580/22 Feb/Mar 2025, Question 23: Exponential Equations
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 6 marks
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The question, in short
Simplify a fractional power expression, then solve an exponential equation involving 16ˣ, (1/2)ˣ and 4ˣ⁺³ to find x.
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Part (a) · 2 marks
Simplify (x² ÷ 4)^(3/2), giving the result in its simplest form.
- 1(x²/4)^(3/2) = (√(x²/4))³ = (x/2)³
- 2= x³/8
Answerx³/8
Part (b) · 4 marks
Solve 16ˣ × (1/2)ˣ = 4ˣ⁺³ and state the value of x.
- 116ˣ = 2⁴ˣ, (1/2)ˣ = 2⁻ˣ, 4ˣ⁺³ = 2²⁽ˣ⁺³⁾
- 22⁴ˣ × 2⁻ˣ = 2³ˣ, so 3x = 2(x + 3)
- 33x = 2x + 6
- 4x = 6
Answer6
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