Difference between revisions of "2002 AMC 12P Problems/Problem 21"

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== Solution ==
 
== Solution ==
We may rewrite the given equation as <math>2(\frac {log c}{log a} + \frac {log c}{log b})</math>
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We may rewrite the given equation as <math>2(\frac {\log c}{\log a} + \frac {\log c}{\log b})</math>
  
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2002|ab=P|num-b=20|num-a=22}}
 
{{AMC12 box|year=2002|ab=P|num-b=20|num-a=22}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 14:49, 10 March 2024

Problem

Let $a$ and $b$ be real numbers greater than $1$ for which there exists a positive real number $c,$ different from $1$, such that

\[2(\log_a{c} + \log_b{c}) = 9\log_{ab}{c}.\]

Find the largest possible value of $\log_a b.$

$\text{(A) }\sqrt{2} \qquad \text{(B) }\sqrt{3} \qquad \text{(C) }2 \qquad \text{(D) }\sqrt{6} \qquad \text{(E) }3$

Solution

We may rewrite the given equation as $2(\frac {\log c}{\log a} + \frac {\log c}{\log b})$

See also

2002 AMC 12P (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
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 12 Problems and Solutions

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