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Exponential and logarithmic equationsEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

  • How do you solve a^{x}=b?
  • State the power rule for logarithms.
  • Solve 5^{x}=40 to 3 s.f.
  • Exact solution of a^{x}=b as a logarithm?
  • State the change of base formula.
  • Write \log{3}20 using \ln.
  • First step in 2^{3x-1}=3 after taking logs?
  • Solve 2^{3x-1}=3 to 3 s.f.
  • Can a^{x}=b be solved if b\leq0 (for a0)?
  • Solve 4^{x}=0.3 to 3 s.f.
  • How do you solve 3^{x}=2^{x+1}?
  • Why can you not write 5^{x}=40\Rightarrow x=8?
  • Investment V=2500\times1.04^{t} reaches £4000: what is the first step?

Exam questions on Exponential and logarithmic equations

  1. Consider the equation 5x=405^{x}=40.
    Show that x=log⁡1040log⁡105x=\frac{\log_{10}40}{\log_{10}5}.2 marks
  2. Consider the equation 23x−1=32^{3x-1}=3.
    Solve 32x+1=503^{2x+1}=50, giving your answer to 3 significant figures.2 marks
  3. The value, £VV, of an investment after tt years is modelled by V=2500×1.04tV=2500\times1.04^{t}.
    Find the time taken for the value to reach £4000. Give your answer in years to 3 significant figures.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).