Find the domain of g(x)=log(2x-3)-ln(x) algebraically

[oryandaw]

Hi Im having problems with this question from my home work..
The instructions say find the domain of the given function algebraically(not graphically)
g(x)=log(2x-3)-ln(x)

I would know how to do it without the ln(x) but im not sure how to do it with it

 

[royhaas]

Re: Find the domain algebraically

The arguments of the logarithm functions must be positive.

 

[oryandaw]

Re: Find the domain algebraically

what?

 

[stapel]

what?

You should have learned about functions, domains, and logarithms back in algebra.

Which topic(s) did you not cover? (We can provide lesson links, but it would help if you narrowed down the search parameters.) Thank you!

Eliz.

 

[galactus]

Re: Find the domain algebraically

What Roy is trying to say is you can not have a negative in a log. i.e. log(-1)=big no-no.
So, of course, those will not be in the domain.

 

[cadamcross]

Re: Find the domain algebraically

Unless otherwise stated, the domain of a function is assumed to be the set of points over which it is well-defined. For log(2x-3)-ln(x) to make sense both log(2x-3) and ln(x) must be defined (separately). The question is this: for a given x, is log(2x-3) defined? Is ln(x) defined?