How do you solve 7e^{x} = 9- e^{- x}7ex=9−e−x?

1 Answer
Salvatore I.
Nov 13, 2016

Two solutions
x_1=ln((9-root2(53))/14)x1=ln(9−2√5314)
x_2=ln((9+root2(53))/14)x2=ln(9+2√5314)

Explanation:

Let's rewrite the equation
7e^x-9+1/e^x=07ex−9+1ex=0
We can multiply both sides for e^xex so that we get

7e^(2x)-9e^x+1=07e2x−9ex+1=0
this can be solved as an ordinary second degree eqaution

e^x=(9+-root2(81-28))/14ex=9±2√81−2814

and consequently

x=ln((9+-root2(53))/14)x=ln(9±2√5314)

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