Calculate : x/y

**dhiab** · December 16th 2009, 06:11 AM

If : $2Ln(x-2y)=Ln(x)+Ln(y)$
Find : $\frac{x}{y}$

**mathaddict** · December 16th 2009, 06:16 AM

Originally Posted by dhiab

If : $2Ln(x-2y)=Ln(x)+Ln(y)$
Find : $\frac{x}{y}$

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)

**dhiab** · December 16th 2009, 06:21 AM

Originally Posted by mathaddict

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

**mathaddict** · December 16th 2009, 06:35 AM

Originally Posted by dhiab

If : $2Ln(x-2y)=Ln(x)+Ln(y)$
Find : $\frac{x}{y}$

Oh ,

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

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

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

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

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

$<br /> x-y=0\Rightarrow \frac{x}{y}=1<br />$

**dhiab** · December 16th 2009, 06:57 AM

HELLO mathaddict
The case x = y is impossibl
Know x>0 , y>0 , x-2y>0
Conclusion x>2y
x >y

**mathaddict** · December 16th 2009, 07:07 AM

Originally Posted by dhiab

HELLO mathaddict
The case x = y is impossibl
Know x>0 , y>0 , x-2y>0
Conclusion x>2y
x >y

hey dhiab, yeah of course , i miss that . Thanks dude .

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