What is the answer to e^x+e^{-x}=5 ?

The answer to e^x+e^{-x}=5 is x=ln((5+sqrt(21))/2),x=ln((5-sqrt(21))/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^x+e^{-x}=5

e^{x} + e^{- x} = 5

x = ln (\frac{5 + 21}{2}), x = ln (\frac{5 - 21}{2})

Decimal Notation

x = 1.56679 \dots, x = - 1.56679 \dots

Solution steps

e^{x} + e^{- x} = 5

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 5

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 5

Solve

u + u^{- 1} = 5 : u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{5 + 21}{2} : x = ln (\frac{5 + 21}{2})

Solve

e^{x} = \frac{5 - 21}{2} : x = ln (\frac{5 - 21}{2})

x = ln (\frac{5 + 21}{2}), x = ln (\frac{5 - 21}{2})

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

- 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

What is the answer to e^x+e^{-x}=5 ?
The answer to e^x+e^{-x}=5 is x=ln((5+sqrt(21))/2),x=ln((5-sqrt(21))/2)