What is the answer to solvefor x,2t=e^x-e^{-x} ?

The answer to solvefor x,2t=e^x-e^{-x} is x=ln(t+sqrt(t^2+1)),x=ln(t-sqrt(t^2+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor x,2t=e^x-e^{-x}

solve for

x, 2 t = e^{x} - e^{- x}

x = ln (t + t^{2} + 1), x = ln (t - t^{2} + 1)

Solution steps

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

Apply exponent rules

2 t = e^{x} - (e^{x})^{- 1}

Rewrite the equation with

e^{x} = u

2 t = u - u^{- 1}

Solve

2 t = u - u^{- 1} : u = t + t^{2} + 1, u = t - t^{2} + 1

u = t + t^{2} + 1, u = t - t^{2} + 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = t + t^{2} + 1 : x = ln (t + t^{2} + 1)

Solve

e^{x} = t - t^{2} + 1 : x = ln (t - t^{2} + 1)

x = ln (t + t^{2} + 1), x = ln (t - t^{2} + 1)

e^{2} x = 2 e^{x}

7^{x^{2} + 2 x} = 4 9^{- 3 x - 5}

2^{4 x - 1} = 3 2^{x + 1}

e^{2 x} = e^{3 - x}

x, 2^{x} + 2^{y} = 10

What is the answer to solvefor x,2t=e^x-e^{-x} ?
The answer to solvefor x,2t=e^x-e^{-x} is x=ln(t+sqrt(t^2+1)),x=ln(t-sqrt(t^2+1))