e^(x) - e^(-x) - 10 = 0

Having some trouble solving for x on this one.

Question

e^(x) - e^(-x) - 10 = 0

Having some trouble solving for x on this one.

anonymous · Answer

can be verified why here: http://en.wikipedia.org/wiki/Hyperbolic_function $$\frac{ e^x - e^{-x} }{ 2 } = \sinh(x)$$

anonymous · Answer

your calculator should have the sinh^{-1} function

experimentx · Answer

make use of inverse hyperbolic function

anonymous · Answer

This question is from a chapter on logarithmic and exponential functions--before the hyperbolic function is introduced.  Is that the only way to solve for x?

anonymous · Answer

Alternatively, you can treat this as a quadratic:
$$e^x-\frac{1}{e^x}-10=0\
e^{2x}-1-10e^x=0$$
Substitute $y=e^x$:
$$y^2-10y-1=0$$

anonymous · Answer

Yeah, that is more what I was looking for

anonymous · Answer

lol

anonymous · Answer

So you're multiplying both sides by e^x? Ok--I see it now.  Thanks.