Solve the exponential equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

[e^(x) - e^(-x)]/2 = -2

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- Aug 10th 2008, 06:26 AMmagentaritaExponential Equation With Number e
Solve the exponential equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

[e^(x) - e^(-x)]/2 = -2

- Aug 10th 2008, 06:47 AMskeeter
$\displaystyle \frac{e^x - e^{-x}}{2} = -2$

multiply both sides by 2 ...

$\displaystyle e^x - e^{-x} = -4$

multiply every term by $\displaystyle e^x$ ...

$\displaystyle (e^x)^2 - 1 = -4e^x$

$\displaystyle (e^x)^2 + 4e^x - 1 = 0$

let $\displaystyle u = e^x$

$\displaystyle u^2 + 4u - 1 = 0$

use the quadratic formula to solve for u, then use the natural log (ln) to solve for x. - Aug 10th 2008, 11:24 AMmagentaritaVery good...
I can take it from here.

Good job!