Difference between revisions of "2002 AMC 12P Problems/Problem 1"

Revision as of 23:17, 29 December 2023

Problem

Which of the following numbers is a perfect square?

$\text{(A) }4^4 5^5 6^6 \qquad \text{(B) }4^4 5^6 6^5 \qquad \text{(C) }4^5 5^4 6^6 \qquad \text{(D) }4^6 5^4 6^5 \qquad \text{(E) }4^6 5^5 6^4$

Solution 1

If $\log_{b} 729 = n$ , then $b^n = 729$ . Since $729 = 3^6$ , $b$ must be $3$ to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of $b \Longrightarrow \boxed{\mathrm{E}}$ .

2002 AMC 12P (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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 == See also ==
-{{AMC12 box|year=2000|num-b=6|num-a=8}}
+{{AMC12 box|year=2002|ab=P|num-b=First question|num-a=2}}
 {{MAA Notice}}

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Difference between revisions of "2002 AMC 12P Problems/Problem 1"

Revision as of 23:17, 29 December 2023

Problem

Solution 1

See also