Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 13, 2011"

Latest revision as of 21:02, 12 June 2011

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)

$8=2^3$ Thus, we add 3 to the exponent.

$2^{x+5}=2^{2x+11}$

Then, we can divide both sides by the left side.

$1=2^{(2x+11)-(x+5)}=2^{x+6}$

$1=2^0$ Therefore,

$0=x+6$

$x=\boxed{-6}$

@@ Line 2: / Line 2: @@
 {{:AoPSWiki:Problem of the Day/June 13, 2011}}
 ==Solution==
-{{potd_solution}}
+First, we can simplify the fraction on the right side of the equation by subtracting the exponents of both numbers.
+<math>{\dfrac{2^{3x+7}}{2^{x-1}}=2^{(3x+7)-(x-1)}=2^{2x+8}</math>
+<math>8=2^3</math> Thus, we add 3 to the exponent.
+<math>2^{x+5}=2^{2x+11}</math>
+Then, we can divide both sides by the left side.
+<math>1=2^{(2x+11)-(x+5)}=2^{x+6}</math>
+<math>1=2^0</math> Therefore,
+<math>0=x+6</math>
+<math>x=\boxed{-6}</math>