Exponential Equation With Number e

**magentarita** · August 10th 2008, 06:26 AM

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

**skeeter** · August 10th 2008, 06:47 AM

$\frac{e^x - e^{-x}}{2} = -2$

multiply both sides by 2 ...

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

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

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

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

let $u = e^x$

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

use the quadratic formula to solve for u, then use the natural log (ln) to solve for x.

**magentarita** · August 10th 2008, 11:24 AM

I can take it from here.

Good job!

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Exponential Equation With Number e

Very good...

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