TMUA · Paper 1: Applications of Mathematical Knowledge

Exponentials and logarithms

18 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 18 questions

  1. What is the value of ?
  2. Solve . What is ?
  3. What is the sum of all real solutions of ?
  4. Given that and , which expression equals ?
  5. What is the exact value of ?
  6. What is the sum of all real solutions of ?
  7. Solve . What is ?
  8. How many real solutions does the equation have?
  9. What is the value of ?
  10. It is given that and . What is the value of ?
  11. Solve . What is ?
  12. What is the smallest integer for which ?
  13. What is the value of ?
  14. What is the product of the real solutions of ?
  15. The curve crosses the -axis at the point . What is ?
  16. A population starts at and doubles every years. After how many years is it first ?
  17. Solve . What is ?
  18. It is given that and . What is ?

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