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Solving exponential equationsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

  • What is an exponential equation?
  • First step for a^x=b when the bases cannot be matched?
  • State the power law of logarithms.
  • Solution of a^x=b using \lg?
  • Solution of e^x=b?
  • Solve 5^x=40 to 3 s.f.
  • Why can a^x=b have no real solution if b\le0?
  • First step in 3e^{2x}=21?
  • Solve 3^{x}=27 without logarithms.
  • Is \frac{\lg40}{\lg5} equal to \lg8?
  • How do you find the doubling time for growth factor a per unit time?
  • 1.035^n=2.5: why is the answer to 'smallest whole number of years' 27, not 26.6?

Exam questions on Solving exponential equations

  1. The equation 5x=405^x=40 is to be solved using logarithms.
    Hence, or otherwise, solve 5x−1=405^{x-1}=40, giving your answer to 3 significant figures.2 marks
  2. £2000 is invested in an account that pays 3.5% compound interest per year. After nn complete years the value of the investment is £2000×1.035n2000\times1.035^n.
    Find the smallest whole number of years after which the investment is worth more than £5000.2 marks
  3. Two equations are given: 43x−1=1004^{3x-1}=100 and 3e2x=213\mathrm{e}^{2x}=21.
    Solve 43x−1=1004^{3x-1}=100, giving your answer 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).