Find the domain of f...?

Question

f(x) = (7)/(2+ln(5x))

Answer 1

There are two things to worry about here: The domain of the natural log function and the denominator of the fraction. First, the domain of the natural log function is (0,INF). (NOT including zero!) Second, if 2+ln(5x)=0, you have division by zero. So we want to find where ln(5x)=-2. This happens when 5x=e^-2, in other words, when x=1/(5*e^2). So finally, the domain is all positive reals except 1/(5*e^2).

Answer 2

1) 0 and negative numbers don´t have ln so x>0 is the first condition
The denominator can´t be 0 so
you must exclude
2+ln(5x)=0 so ln(5x)= -2 and x = 1/5* e^-2
so the domain is x>0 excluding x= 1/5 e^-2

Answer 3

Note that when you plug in 0, you get a real number, which is 7/3. If you plug in any value higher than 0, in other words, any positive number, it just yields a number. So now you know that 0 and every positive number is part of the domain of this function.

However, notice that if you plug in a negative number, you have to take the ln of a negative number. You can't take the ln of a negative number. Hence it would be undefined.

So the answer to this question is

Domain: 0 to infinite, inclusive of 0.

Answer 4

I think you wrote the problem wrong. Cause, okay, you first set 2+ln(5x)=0 and then that equals to ln(5x)=-2 And then 5x = e^-2 and well, it just doesn't make sense...maybe it's x is all real numbers except (e^-2)/5.