What is the answer to e^x+e^{-x}=3 ?

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

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e^x+e^{-x}=3

e^{x} + e^{- x} = 3

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

Decimal Notation

x = 0.96242 \dots, x = - 0.96242 \dots

Solution steps

e^{x} + e^{- x} = 3

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 3

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 3

Solve

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

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

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

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

4^{x + 3} \cdot 8^{2 x - 1} = 2

2^{2 x} + 2^{x} - 12 = 0

e^{x} + x e^{x} = 0

3 (4^{x}) = 4 (5^{2 x - 7})

2^{x - 5} = 3

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