Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 13, 2011"
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| + | First, we can simplify the fraction on the right side of the equation by subtracting the exponents of both numbers. | ||
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| + | <math>{\dfrac{2^{3x+7}}{2^{x-1}}=2^{(3x+7)-(x-1)}=2^{2x+8}</math> | ||
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| + | <math>8=2^3</math> Thus, we add 3 to the exponent. | ||
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| + | <math>2^{x+5}=2^{2x+11}</math> | ||
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| + | Then, we can divide both sides by the left side. | ||
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| + | <math>1=2^{(2x+11)-(x+5)}=2^{x+6}</math> | ||
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| + | <math>1=2^0</math> Therefore, | ||
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| + | <math>0=x+6</math> | ||
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| + | <math>x=\boxed{-6}</math> | ||
Revision as of 20:33, 12 June 2011
Problem
AoPSWiki:Problem of the Day/June 13, 2011
Solution
This Problem of the Day needs a solution. If you have a solution for it, please help us out by adding it. First, we can simplify the fraction on the right side of the equation by subtracting the exponents of both numbers.
${\dfrac{2^{3x+7}}{2^{x-1}}=2^{(3x+7)-(x-1)}=2^{2x+8}$ (Error compiling LaTeX. Unknown error_msg)
Thus, we add 3 to the exponent.
Then, we can divide both sides by the left side.
Therefore,
