Difference between revisions of "2004 AMC 12B Problems/Problem 3"
(New page: == Problem == If <math>x</math> and <math>y</math> are positive integers for which <math>2^x3^y=1296</math>, what is the value of <math>x+y</math>? <math>(\mathrm {A}) 8\qquad (\mathrm {B...) |
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If <math>x</math> and <math>y</math> are positive integers for which <math>2^x3^y=1296</math>, what is the value of <math>x+y</math>? | If <math>x</math> and <math>y</math> are positive integers for which <math>2^x3^y=1296</math>, what is the value of <math>x+y</math>? | ||
| − | <math>(\mathrm {A}) 8\qquad (\mathrm {B}) 9 \qquad (\mathrm {C}) 10 \qquad (\mathrm {D}) 11 \qquad (\mathrm {E}) 12</math> | + | <math>(\mathrm {A})\ 8 \qquad (\mathrm {B})\ 9 \qquad (\mathrm {C})\ 10 \qquad (\mathrm {D})\ 11 \qquad (\mathrm {E})\ 12</math> |
== Solution == | == Solution == | ||
<math>1296 = 2^4 3^4</math> and <math>4+4=\boxed{8} \Longrightarrow \mathrm{(A)}</math>. | <math>1296 = 2^4 3^4</math> and <math>4+4=\boxed{8} \Longrightarrow \mathrm{(A)}</math>. | ||
| + | |||
| + | == Video Solution 1== | ||
| + | https://youtu.be/So54Ar_fxdE | ||
| + | |||
| + | ~Education, the Study of Everything | ||
== See Also == | == See Also == | ||
{{AMC12 box|year=2004|ab=B|num-b=2|num-a=4}} | {{AMC12 box|year=2004|ab=B|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 18:21, 22 October 2022
Contents
Problem
If 
and 
are positive integers for which 
, what is the value of 
?
Solution
and 
.
Video Solution 1
~Education, the Study of Everything
See Also
| 2004 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 2 |
Followed by Problem 4 |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
