Difference between revisions of "2010 AMC 12A Problems/Problem 11"
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This problem is quickly solved with knowledge of the laws of exponents and logarithms. | This problem is quickly solved with knowledge of the laws of exponents and logarithms. | ||
| − | < | + | <cmath>\begin{align*} 7^{x+7} &= 8^x \\ |
| + | 7^x*7^7 &= 8^x \\ | ||
| + | \left(\frac{8}{7}\right)^x &= 7^7 \\ | ||
| + | x &= \log_{8/7}7^7 \end{align*}</cmath> | ||
| − | <math> 7 | + | Since we are looking for the base of the logarithm, our answer is <math>\boxed{\textbf{(C)}\ \frac{8}{7}}</math>. |
| − | + | == See also == | |
| + | {{AMC12 box|year=2010|num-b=10|num-a=12|ab=A}} | ||
| − | + | [[Category:Introductory Number Theory Problems]] | |
| − | |||
| − | |||
Revision as of 22:28, 25 February 2010
Problem
The solution of the equation 
can be expressed in the form 
. What is 
?
Solution
This problem is quickly solved with knowledge of the laws of exponents and logarithms.
Since we are looking for the base of the logarithm, our answer is 
.
See also
| 2010 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 10 |
Followed by Problem 12 |
| 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 | |
