# Simplifying Ln(x)

• May 9th 2012, 04:25 PM
VanBuren
Simplifying Ln(x)
Hey all i'm having a tough time simplifying this:

nln(1/y1)-nln(1/y2)+((1/y1)-(1/y2))(ln(x1)+ln(x2)+...ln(xn))

yuck!
• May 9th 2012, 05:17 PM
HallsofIvy
Re: Simplifying Ln(x)
I can't say what you would consider "simpler" but, using the properties of logarithms, that is
$ln\left(\left(\frac{y_2}{y_1}\right)^n\left(x_1x_2 \cdot\cdot\cdot xn\right)^{\frac{y_2- y_1}{y_1y_2}}\right)$
• May 9th 2012, 06:20 PM
VanBuren
Re: Simplifying Ln(x)
[FONT=Arial]Hey thanks for the speedy response, this is actually a smaller part of a much larger stats question I have....

chi-squared distribution=

with

where Y is actually theta

I need to develop a method for testing H0 : θ = θ0 against H0 : θ = θ1 where 0 < θ0 < θ1 < 1
But i'm stuck, i plugged the moment generating function into the formula for chi-squared but have no idea if simplifying is even the right direction... i'm not dumb i'm just stuck... help!
• May 9th 2012, 06:28 PM
VanBuren
Re: Simplifying Ln(x)
Here is the likelihood function of Y sub whatever:

http://www.texify.com/img/%5CLARGE%5...n%7D%29%29.gif