Difference between revisions of "2005 AMC 12B Problems/Problem 13"
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== See also == | == See also == | ||
{{AMC12 box|year=2005|ab=B|num-b=12|num-a=14}} | {{AMC12 box|year=2005|ab=B|num-b=12|num-a=14}} | ||
| + | {{MAA Notice}} | ||
Revision as of 09:41, 4 July 2013
Problem
Suppose that 
, 
, 
, ... , 
. What is 
?
Solution
We see that we can re-write , , , ... , as 
by using substitution. By using the properties of exponents, we know that 
.
$\begin{align*}4^{x_1x_2...x_{124}}=128\\2^{2x_1x_2...x_{124}}=2^7\\2x_1x_2...x_{124}=7\\x_1x_2...x_{124}=\dfrac{7}{2}\end{align*}$ (Error compiling LaTeX. Unknown error_msg)
Therefore, the answer is 
See also
| 2005 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 12 |
Followed by Problem 14 |
| 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. 
