IMC 2006 Q18
18. Given that \(4^x + 4^x + 4^x + 4^x = 4^{16}\), what is the value of \(x\)?
- A 2
- B 4
- C 8
- D 12
- E 15
Intermediate Mathematical Challenge 2006, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 15
Note that \(4^x + 4^x + 4^x + 4^x = 4 \times 4^x = 4^{x+1}\). So \(x + 1 = 16\).
Solution © UK Mathematics Trust, from the IMC 2006 solutions.