IMC 2014 Q19
19. Suppose that \(8^m = 27\). What is the value of \(4^m\)?
- A 3
- B 4
- C 9
- D 13.5
- E there is no such \(m\)
Intermediate Mathematical Challenge 2014, Question 19. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 9
Note that \(8^m = (2^3)^m = 2^{3m} = (2^m)^3\) and \(27 = 3^3\); so \(2^m = 3\). Therefore \(4^m = 2^m \times 2^m = 9\).
Solution © UK Mathematics Trust, from the IMC 2014 solutions. Longer versions with investigations: Solutions and investigations (PDF).