Understanding the Domain of 10/ln x: A Guide for Confused Learners

[Rusho]

I'm confused on this domain question

10/ln x

I really don't know where to start. Do I graph it and then go from there?

 

[vsage]

what's the domain of ln(x)?

 

[Rusho]

0, infinity

 

[dav2008]

Basically I take it you are looking for the set of all x values for which the expression 10/ln(x) is defined, correct?

So think to yourself, when is that expression not defined?

(When you answered "0,infinity", did you mean (0,infinity)?)

 

[Rusho]

well if it equals -10, then I think that would make the numerator zero.

But I think I need to look at the denominator. So it cannot be zero

 

[HallsofIvy]

well if it equals -10, then I think that would make the numerator zero.

But I think I need to look at the denominator. So it cannot be zero

Yes, that's true. For what value of x is ln x= 0?

Also, the domain of ln x is the open interval $(0, \infty)$.
Your "0, infinity" is ambiguous. 0 is not in the domain of ln x.