Question

Solve the logarithmic equation. Express your solutions in exact form only.
18e^-x -e^x=7
18/e^x - e^x = 7
let e^x = a

18/a - a - 7 = 0
18 - a^2 - 7a = 0
a^2 + 7a - 18 = 0
(a+9)(a-2) = 0
a = -9 or a = 2
then
e^x = -9 ----> no solution
or
e^x = 2
x = ln 2

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