# Continuity homework problem

1. Apr 12, 2010

### evagelos

how can we prove that lun x is continuous over (0, $$\infty$$ )?

Provided that we define : lun x =y <=> $$e^y =x$$?

2. Apr 12, 2010

### mathman

Re: continuity

lnx - lnu = ln(x/u). For any fixed x > 0, u->x => x/u -> 1 and ln1=0.

You can dress this proof up.

3. Apr 12, 2010

### evagelos

Re: continuity

Can you elaborate a little more ? I do not how to start

4. Apr 13, 2010

### mathman

Re: continuity

I am not sure what you are given to start with. For example are you assuming ey is continuous? My proof (I admit) is somewhat flawed. It needs continuity of ln(x) for x=1, which then implies continuity for all x.