How to solve 2e^x -1 = 21e^(-x)?

1 Answer
Dec 7, 2017

See below.

Explanation:

21e^(-x)=21/e^x

2e^x-21/e^x-1=0

Let y=e^x

2y-21/y-1=0

2y^2-y-21=0

Factor:

(2y-7)(y+3)=0=>y=7/2 and y=-3

( -3 would give complex solution)

If y=7/2

e^x=7/2

x=ln(7/2)

If y=-3

e^x=-3

x=ln(-3)