Problem:
Find the value of x that satisfies the equation
25−2=526/x⋅2517/x548/x
Answer Choices:
A. 2
B. 3
C. 5
D. 6
E. 9
Solution:
Write all the terms with the common base 5. Then
5−4=25−2=526/x⋅2517/x548/x=526/x⋅534/x548/x=5(48−26−34)/x=5−12/x
It follows that −x12=−4, so x=3.
OR
First write 25 as 52. Raising both sides to the x power gives
5−4x=526534548=548−26−34=5−12
So −4x=−12 and x=3.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions