2002 AMC 12B Problems/Problem 22
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:
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Solution 3
Note that . is also equal to . So . By the change of bases formula, . Following the same reasoning, , and so on.
Now solving for , we see that it equals
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See also
2002 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
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All AMC 12 Problems and Solutions |
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