Difference between revisions of "2003 AMC 12A Problems/Problem 23"
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+ | == Problem 23 == | ||
+ | |||
+ | If <math>a\geq b > 1,</math> what is the largest possible value of <math>\log_{a}(a/b) + \log_{b}(b/a)?</math> | ||
+ | |||
+ | <math> | ||
+ | \mathrm{(A)}\ -2 \qquad | ||
+ | \mathrm{(B)}\ 0 \qquad | ||
+ | \mathrm{(C)}\ 2 \qquad | ||
+ | \mathrm{(D)}\ 3 \qquad | ||
+ | \mathrm{(E)}\ 4 | ||
+ | </math> | ||
+ | |||
== Solution == | == Solution == | ||
Revision as of 18:34, 22 February 2010
Problem 23
If what is the largest possible value of
Solution
Using logarithmic rules, we see that
Since and
are both positive, using AM-GM gives that the term in parentheses must be at least
, so the largest possible values is