What is the answer to e^x+e^{-x}=4 ?

The answer to e^x+e^{-x}=4 is x=ln(2+sqrt(3)),x=ln(2-sqrt(3))

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e^x+e^{-x}=4

e^{x} + e^{- x} = 4

x = ln (2 + 3), x = ln (2 - 3)

Solution steps

e^{x} + e^{- x} = 4

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 4

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 4

Solve

u + u^{- 1} = 4 : u = 2 + 3, u = 2 - 3

u = 2 + 3, u = 2 - 3

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

x = ln (2 + 3), x = ln (2 - 3)

30 = 1 0^{x}

64 \cdot 1 6^{- 3 x} = 1 6^{3 x - 2}

12 5^{2 - 3 x} = 5

3^{x} = 27

3^{x} + 3^{(3 - x)} = 12

What is the answer to e^x+e^{-x}=4 ?
The answer to e^x+e^{-x}=4 is x=ln(2+sqrt(3)),x=ln(2-sqrt(3))