2010 AMC 12A Problems/Problem 11
Problem
The solution of the equation can be expressed in the form
. What is
?
Solution 1
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 .
Solution 2
First, take the of both sides, which gives us
. We move the
terms to 1 side.
. Isolate
and manipulate the answer. $x=\frac{7}{log_{7}\frac{8}{7}=7log_{\frac{8}{7}}7=log_{\frac{8}{7}}7^7. Therefore, the answer is$ (Error compiling LaTeX. Unknown error_msg)\frac{8}{7}=\fbox{C}$
Video Solution1 (Clever Manipulations)
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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 |
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