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Math Help - Finding the domain of ln Functions

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by Bryn View Post
    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
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  3. #3
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    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
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  4. #4
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    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?
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