2005 AMC 10B Problems/Problem 17
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Contents
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 3 (logarithm chain rule)
As in Solution 2, we can write as
,
as
,
as
, and
as
.
is equivalent to
. By the logarithm chain rule, this is equivalent to
, which evaluates to
.
~solver1104
See Also
2005 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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All AMC 10 Problems and Solutions |
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