Posted by **ayonna** on Wednesday, March 27, 2013 at 12:48am.

solve the following exponential equation:show your work.

e^x-e^-x/2=7

1. write exact answer.

2.write answer approximated to 3 decimal places.

whaaaat? smh I don't get it at all.

- math -
**Steve**, Wednesday, March 27, 2013 at 10:43am
If you mean

(e^x - e^-x)/2 = 7

e^x - e^-x = 14

e^2x - 1 = 14e^x

e^2x - 14e^x - 1 = 0

Now you just have a quadratic in e^x, so

e^x = (14±√200)/2

= 7±5√2

e^x is never negative, so

e^x = 7+5√2

x = ln(7+5√2) = 2.644

Or, more directly, recognize that what you have is

sinh(x) = 7

x = 2.644

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