What is the answer to e^x+e^{-x}=7 ?

The answer to e^x+e^{-x}=7 is x=ln((7+3sqrt(5))/2),x=ln((7-3sqrt(5))/2)

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e^x+e^{-x}=7

e^{x} + e^{- x} = 7

x = ln (\frac{7 + 3 5}{2}), x = ln (\frac{7 - 3 5}{2})

Decimal Notation

x = 1.92484 \dots, x = - 1.92484 \dots

Solution steps

e^{x} + e^{- x} = 7

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 7

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 7

Solve

u + u^{- 1} = 7 : u = \frac{7 + 3 5}{2}, u = \frac{7 - 3 5}{2}

u = \frac{7 + 3 5}{2}, u = \frac{7 - 3 5}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{7 + 3 5}{2} : x = ln (\frac{7 + 3 5}{2})

Solve

e^{x} = \frac{7 - 3 5}{2} : x = ln (\frac{7 - 3 5}{2})

x = ln (\frac{7 + 3 5}{2}), x = ln (\frac{7 - 3 5}{2})

- 2 e^{- x^{2}} x = 0

x, b e^{- 2 x} + 3 y + 3 x = 0

2 x^{4} \cdot e^{- 2 x} = 0

7 + 15 e^{1 - 3 x} = 37

4^{x + 3} = 8^{x - 2}

What is the answer to e^x+e^{-x}=7 ?
The answer to e^x+e^{-x}=7 is x=ln((7+3sqrt(5))/2),x=ln((7-3sqrt(5))/2)