Markquill
Start free

CAIE A Level Mathematics 9709

Logarithmic and exponential functions questions

Exam-style questions on Logarithmic and exponential functions, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

Practise this topic free

Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 3 marksFoundationSolve the inequality 2^x < 8.
  2. 3 marksStandardThe variables x and y are related by y = k a^x. When ln y is plotted against x, the resulting straight line has gradient 1.60944 and intercept 1.38629. Find the value of a.
  3. 4 marksStandardSolve the equation ln(x+1) + ln(x+3) = ln(15).
  4. 4 marksStandardSolve the equation 5^2x - 2 = 4^1x - 1 for x. Give your answer correct to 3 significant figures.
  5. 3 marksStandardSolve for x, where x 1: log 3 x + log 3 (x - 1) = log 3 20.
  6. 2 marksStandardIt is given that 5 × 10^x = 5000.
  7. 2 marksChallengeA radioactive sample decays according to N = 640 × 0.5^t, where N is the amount remaining after t half-lives.
  8. 4 marksChallengeIn an experiment, the variables x and y are believed to satisfy the equation y = k x^n. A graph of ln y against ln x is plotted, and it is found to be a straight line passing through the points ( 2, 2 ) and ( 4, 10 )…