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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

solve for

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

t = ln (\frac{x + x ^{2} - 4}{2}), t = ln (\frac{x - x ^{2} - 4}{2})

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{t} = u

x = u + u^{- 1}

Solve

x = u + u^{- 1} : u = \frac{x + x ^{2} - 4}{2}, u = \frac{x - x ^{2} - 4}{2}

u = \frac{x + x ^{2} - 4}{2}, u = \frac{x - x ^{2} - 4}{2}

Substitute back

u = e^{t},

solve for

t

Solve

e^{t} = \frac{x + x ^{2} - 4}{2} : t = ln (\frac{x + x ^{2} - 4}{2})

Solve

e^{t} = \frac{x - x ^{2} - 4}{2} : t = ln (\frac{x - x ^{2} - 4}{2})

t = ln (\frac{x + x ^{2} - 4}{2}), t = ln (\frac{x - x ^{2} - 4}{2})

121 + 4 (5^{3 - x}) = 5^{x}

4 = 3^{x}

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

3^{x + 1} - 3^{x - 1} = 72

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

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