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Solving equation with natural log with inverse hyperbolic

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve ln(sinh-1(x)) = 1
    (Just give the formula for x, no calculator is necessary)
    sinh-1(x) = asinh


    2. Relevant equations



    3. The attempt at a solution

    When I did this, I knew sinh-1(x) = ln(x + sqrt.(x^2 +1), but the equation would look like
    ln(ln(x + sqrt.(x^2 + 1 )) = 1, which looks weird because I don't what to do afterwards
    So then I tried exponentiate both sides and it will be asinh(x) = e then multiplying both sides by sinh, so my answer is x = sinhe, is this right?
     
  2. jcsd
  3. Dec 6, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You do NOT 'multiply both sides by sinh'- there is no multiplication involved here! After you take the exponential of both sides you have sinh-1(x)= e. Now take sinh of both sides of that: sinh(sinh-1(x))= sinh(e).

    What is sinh(sinh-1(x))?
     
  4. Dec 6, 2009 #3
    oh sorry, What i meant was "take" not "multiply" even though i typed multiply -_-

    ok so then, sinh(sinh-1(x)) = sinh-1(sinh(x)) = x ?
     
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