Question

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

Having some trouble solving for x on this one.

Answer 1

can be verified why here: http://en.wikipedia.org/wiki/Hyperbolic_function

\[\frac{ e^x - e^{-x} }{ 2 } = \sinh(x)\]

Answer 2

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

Answer 3

make use of inverse hyperbolic function

Answer 4

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?

Answer 5

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

Answer 6

Yeah, that is more what I was looking for

Answer 7

lol

Answer 8

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