solve exponential equation. express in exact form.

Question

e^x-42e^-x= -19

Answer 1

multiply each term by e^x

(e^x)^2 - 42 + 19e^x = 0
let y = e^x
y^2 + 19y - 42 = 0
(y+21)(y-2) = 0
y = -21 or y = 2

so e^x = 2
x = ln 2

or

e^x = -21, which has no solution

x = ln2

Answer 2

thanks again