Problem:
For what value of x does 10xâ‹…1002x=10005?
Answer Choices:
A. 1
B. 2
C. 3
D. 4
E. 5
Solution:
The equation can be written 10x⋅(102)2x=(103)5 or 10x⋅104x= 1015. Thus 105x=1015, so 5x=15 and x=3​.
The problems on this page are the property of the MAA's American Mathematics Competitions