Simplifying

[Function]

Hello everyone

 

Just messing around with some numbers and formulas, I got to the (pretty useless) idea to simplify [math]\lim_{x\to\infty}{\left[\frac{\log{x^a}+\log{x^b}}{\log{\left(x^a+x^b\right)}}\right]}[/math]

 

The most simplified form I get is (after using the rule of de L'Hôpital once and just using some rules concering calculations with limits)

 

[math]1+\lim_{x\to\infty}{\left[\frac{a\cdot x^b+b\cdot x^a}{a\cdot x^a+b\cdot x^b}\right]}[/math]

 

Is there any way to simplify this even more? Thanks.

 

Function

Edited January 30, 2014 by Function

[mathematic]

numerator = (a+b)logx. Denominator is approx. max(a,b)logx