How do I find the domain and range of the following function: y = ln ln x ?

Question

anonymous · Answer

Wow, the natural log of the natural log of x. You'd have to sit and ask yourself, what x values are impossible for me to take the natural log of, that will show you the domain of y, the range is the all of the possible outcomes of the equation, what's the smallest and largest  values you can get from the natural log?

anonymous · Answer

That's where I'm confused... How would I determine this???

anonymous · Answer

Well, you can't take a log of a negative right?

anonymous · Answer

An easy way is to plot a graph of this, and that may help you determine the answer. And yes! You can also not take the log of 0, so you already know that x must be (0. infinity)

anonymous · Answer

How would I find the range then?

dumbcow · Answer

no for ln x , the domain is (0,infty) and range is All reals

thus the range for "inner" ln x is (0,infty)
ln x > 0
x > 1

--> Domain of ln(ln x) is (1,infty)
--> Range is still All Reals