2002 AMC 12B Problems/Problem 22
Problem
For all integers greater than , define . Let and . Then equals
Solution
Solution 1
By the change of base formula, . Thus
Solution 2
So
\begin{align*} b- c &= \left(log_2002 2 + log_2002 3 + log_2002 4 + log_2002 5 - log_2002 10 - log_2002 11 - log_2002 12 - log_2002 13 - log_2002 14))\\ &= \left(log_2002 (\frac{2 \cdot 3 \cdot 4 \cdot 5}{10 \cdot 11 \cdot 12 \cdot 13 \cdot 14}))\\ &= \left(log_2002 2002^-1) = -1 \Rightarrow \mathrm{(B)} \end{align*} (Error compiling LaTeX. Unknown error_msg)
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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