# Solving equation with natural log with inverse hyperbolic

1. Dec 6, 2009

### yojo95

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. Dec 6, 2009

### HallsofIvy

Staff Emeritus
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))?

3. Dec 6, 2009

### yojo95

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 ?