Question

could someone please help me solve this problem...

e^x - 12e^(-x) - 1

Answer 1

I assume the complete question is:
solve for x:
e^x - 12e^(-x) - 1 = 0

Substitute y=e^x, and e^(-x)=1/e^x=1/y.
e^x - 12e^(-x) - 1 =0
becomes
y-12/y-1 = 0
Since y=e^x, y>0 (i.e. y≠0)
y²-y-12=0
Factor and solve the quadratic.
Reject the negative root, since e^x cannot be negative or zero.
Solve for x.