Question

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.

Answer 1

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