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1-2-x-y-1-2-y-x-4-x-y-




Question Number 10133 by konen last updated on 26/Jan/17
((1+2^(x−y) )/(1+2^(y−x) ))=4⇒x−y=?
$$\frac{\mathrm{1}+\mathrm{2}^{\mathrm{x}−\mathrm{y}} }{\mathrm{1}+\mathrm{2}^{\mathrm{y}−\mathrm{x}} }=\mathrm{4}\Rightarrow\mathrm{x}−\mathrm{y}=? \\ $$
Answered by ridwan balatif last updated on 26/Jan/17
((1+2^(x−y) )/(1+2^(−(x−y)) ))=4  ((1+2^(x−y) )/(1+(1/2^(x−y) )))=4  (((1+2^(x−y) )/(2^(x−y) +1)))×2^(x−y) =4  2^(x−y) =4  2^(x−y) =2^2   x−y=2
$$\frac{\mathrm{1}+\mathrm{2}^{\mathrm{x}−\mathrm{y}} }{\mathrm{1}+\mathrm{2}^{−\left(\mathrm{x}−\mathrm{y}\right)} }=\mathrm{4} \\ $$$$\frac{\mathrm{1}+\mathrm{2}^{\mathrm{x}−\mathrm{y}} }{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{x}−\mathrm{y}} }}=\mathrm{4} \\ $$$$\left(\frac{\mathrm{1}+\mathrm{2}^{\mathrm{x}−\mathrm{y}} }{\mathrm{2}^{\mathrm{x}−\mathrm{y}} +\mathrm{1}}\right)×\mathrm{2}^{\mathrm{x}−\mathrm{y}} =\mathrm{4} \\ $$$$\mathrm{2}^{\mathrm{x}−\mathrm{y}} =\mathrm{4} \\ $$$$\mathrm{2}^{\mathrm{x}−\mathrm{y}} =\mathrm{2}^{\mathrm{2}} \\ $$$$\mathrm{x}−\mathrm{y}=\mathrm{2} \\ $$

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