# Limits question (w/natural logs!)

1. Nov 28, 2008

### Melawrghk

1. The problem statement, all variables and given/known data
Find limit:
limx=> inf (1+2x)11/(2ln(x))

3. The attempt at a solution
Well, I have no real mathematical attempt to this. It was just my common sense that failed. Anyways, I figured that as x goes to infinity the 2ln(x) term will also go to infinity. Since that 11 on the top doesn't change, the term will eventually go to 0. So then we'd have (1+2*infinity) to the power of zero. Which should equal one.

HOWEVER, that's wrong. I think I know why - because the infinity in the base will be different from that in the power (the power one will be increasing slower because of the ln()). But I don't know. I know there should be some mathematical way of doing this, but I don't see. Any tips?

2. Nov 29, 2008

### sutupidmath

ok i;ll give u a hint

$$(1+2x)^\frac{11}{2ln(x)}=e^{\frac{11}{2ln(x)}ln(1+2x)}$$