# Calculate : x/y

• Dec 16th 2009, 06:11 AM
dhiab
Calculate : x/y
If : $\displaystyle 2Ln(x-2y)=Ln(x)+Ln(y)$
Find : $\displaystyle \frac{x}{y}$
• Dec 16th 2009, 06:16 AM
Quote:

Originally Posted by dhiab
If : $\displaystyle 2Ln(x-2y)=Ln(x)+Ln(y)$
Find : $\displaystyle \frac{x}{y}$

2L(x-2y)=Lnx+Lny

2x-4y=nx+ny

2x-nx=ny+4y

x(2-n)=y(4+n)

x/y=(4+n)/(2-n)
• Dec 16th 2009, 06:21 AM
dhiab
Quote:

2L(x-2y)=Lnx+Lny

2x-4y=nx+ny

2x-nx=ny+4y

x(2-n)=y(4+n)

x/y=(4+n)/(2-n)

Hello
Ln(x) is not : L×n×x
Ln(x) is Log
• Dec 16th 2009, 06:35 AM
Quote:

Originally Posted by dhiab
If : $\displaystyle 2Ln(x-2y)=Ln(x)+Ln(y)$
Find : $\displaystyle \frac{x}{y}$

Oh ,

$\displaystyle 2\ln (x-2y)=\ln x+\ln y$

$\displaystyle (x-2y)^2=xy$

$\displaystyle x^2-5xy+4y^2=0$

$\displaystyle (x-4y)(x-y)=0$

$\displaystyle x-4y=0\Rightarrow \frac{x}{y}=4$

$\displaystyle x-y=0\Rightarrow \frac{x}{y}=1$
• Dec 16th 2009, 06:57 AM
dhiab
The case x = y is impossibl
Know x>0 , y>0 , x-2y>0
Conclusion x>2y
x >y
• Dec 16th 2009, 07:07 AM