All flashcards topics

Solving equations of the form a^x = bEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

  • How do you solve a^x=b when the bases cannot be matched?
  • State the change of base formula.
  • Exact solution of a^x=b?
  • Solve 5^x=40 to 3 s.f.
  • Which law brings the index down in \log(a^x)?
  • Does a^x=-4 have a real solution (for a0)?
  • Evaluate \log330 to 3 s.f. using the change of base formula.
  • Why write (2x+1)\log3 with brackets?
  • First step in solving 3^{x+1}=50?
  • How do you solve 7^x=2^{x+3}?
  • Is \frac{\log40}{\log5} equal to \log40-\log5?
  • When should you round in a multi-step logarithm problem?
  • What multiplier models 4% growth per year?

Exam questions on Solving equations of the form a^x = b

  1. The equation 5x=405^x=40 has solution x=kx=k.
    Solve 5x−2=405^{x-2}=40.2 marks
  2. Consider the equation 32x=2003^{2x}=200, where xx is a real number.
    Hence, or otherwise, solve 32x+1=6003^{2x+1}=600.2 marks
  3. Give non-exact answers to 3 significant figures. A calculator may be used.
    Solve 7x=2x+37^x=2^{x+3}.3 marks
See the full worksheet

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).