# Thread: Finding the domain of ln Functions

1. ## Finding the domain of ln Functions

Write down the maximal domain (i.e. the largest possible domain) for the following:
(a) ln(cosh x), (b) ln(coth x), (c) ln(tanh x), (d) ln(ln(ln x))

Having trouble with this, especially d. I have had it explained, so if someone could be really kind and explain it as simply as possible, I would really appreciate it. As for a, b & c. They seem to be all Ln of a exponential function with a domain of all real numbers. Given this, it seems that the domain would be x≥0 as that is the function for Ln. However, the answers I have don't agree. Any ideas - Many thanks

2. Originally Posted by Bryn
Write down the maximal domain (i.e. the largest possible domain) for the following:
(a) ln(cosh x), (b) ln(coth x), (c) ln(tanh x), (d) ln(ln(ln x))
for a, b, and c, determine the value of x that makes each hyperbolic trig function greater than 0

for d ...

$\ln(\ln{x}) > 0$

$\ln{x} > 1$

$x > e$

3. Why is that the case.

I understand that ln(x)>0 but the rest I can't follow

Any other way of explaining it

thanks

4. you know that $\ln 1=0,$ so having any number greater than $1$ will turn that logarithm positive, so as for solving $\ln(\ln x)>0,$ we require that $\ln x>1,$ and we can exponentiate this since $x\mapsto e^x$ is a strictly increasing function, hence $e^{\ln x}>e^1\implies x>e,$ does this make sense?