Difference between revisions of "2002 AMC 12B Problems/Problem 22"
(→Solution 2) |
(→Solution 3) |
||
Line 21: | Line 21: | ||
~yofro | ~yofro | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
== See also == | == See also == |
Latest revision as of 21:30, 23 November 2020
Contents
Problem
For all integers greater than , define . Let and . Then equals
Solution
By the change of base formula, . Thus
Solution 2
Note that . Thus . Also notice that if we have a log sum, we multiply, and if we have a log product, we divide. Using these properties, we get that the result is the following:
~yofro
See also
2002 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.