# Domain question...

• Jan 26th 2010, 09:08 PM
Ferny84
Domain question...
I'm having problems finding the domain of f(x) = ln(4 + ln(x)).

I thought the domain of ln(x) was (0,infinity) but I was wrong.

Can anyone explain how to find the domain of ln(x)?
• Jan 26th 2010, 09:18 PM
VonNemo19
Quote:

Originally Posted by Ferny84
I'm having problems finding the domain of f(x) = ln(4 + ln(x)).

I thought the domain of ln(x) was (0,infinity) but I was wrong.

Can anyone explain how to find the domain of ln(x)?

Well, isn't it the case that $e^y$ will ALWAYS be positive?
• Jan 27th 2010, 03:23 AM
HallsofIvy
Quote:

Originally Posted by Ferny84
I'm having problems finding the domain of f(x) = ln(4 + ln(x)).

I thought the domain of ln(x) was (0,infinity) but I was wrong.

If, by that, you mean x positive, you are right. What makes you think you are wrong?

But, of course, the domain of ln(x) is not necessarily the same as the domain of ln(4+ ln(x)). In order to be able to take the second logarithm, you must have 4+ ln(x)> 0 or ln(x)> -4. For what value of x is ln(x)= -4?

Quote:

Can anyone explain how to find the domain of ln(x)?
You already know that. That's the wrong question!