2005 AMC 10B Problems/Problem 17
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Contents
[hide]Problem
Suppose that 
, 
, 
, and 
. What is 
?
Solution
Solution 2 (logarithms)
We can write 
as 
, 
as 
, 
as 
, and 
as 
.
We know that 
can be rewritten as 
, so we have:
Solution using logarithm chain rule
As in solution 2, we can write as , as 
, as 
, and as 
. 
is equivalent to 
. Note that by the logarithm chain rule, this is equivalent to 
, which evaluates to 
, so 
is the answer.
~solver1104
See Also
| 2005 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 10 Problems and Solutions | ||
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