Difference between revisions of "2002 AMC 12B Problems/Problem 22"
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\qquad\mathrm{(D)}\ \frac{1}{1001} | \qquad\mathrm{(D)}\ \frac{1}{1001} | ||
\qquad\mathrm{(E)}\ \frac 12</math> | \qquad\mathrm{(E)}\ \frac 12</math> | ||
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== Solution == | == Solution == | ||
Revision as of 18:17, 13 January 2022
Contents
Problem
For all integers greater than
, define
. Let
and
. Then
equals
d
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.