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 19:21, 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 |
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