What is the answer to (e^x+e^{-x})/(e^x+1)=4 ?

The answer to (e^x+e^{-x})/(e^x+1)=4 is x=ln((sqrt(7)-2)/3)

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

\frac{e ^{x} + e ^{- x}}{e ^{x} + 1} = 4

x = ln (\frac{7 - 2}{3})

Solution steps

\frac{e ^{x} + e ^{- x}}{e ^{x} + 1} = 4

Multiply both sides by

e^{x} + 1

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

Simplify

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

u + u^{- 1} = 4 (u + 1) : u = - \frac{2 + 7}{3}, u = \frac{7 - 2}{3}

u = - \frac{2 + 7}{3}, u = \frac{7 - 2}{3}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = - \frac{2 + 7}{3} :

No Solution for

x \in R

Solve

e^{x} = \frac{7 - 2}{3} : x = ln (\frac{7 - 2}{3})

x = ln (\frac{7 - 2}{3})

Verify Solutions:

x = ln (\frac{7 - 2}{3})

True

The solution is

x = ln (\frac{7 - 2}{3})

4 e^{2 x} - e^{x} = 0

70 \cdot 2^{3 x} = 35

2^{3 x + 2} = 14

- 2 e^{- x^{2}} = 0

e^{- 5.6 k} + 4 k = 1

What is the answer to (e^x+e^{-x})/(e^x+1)=4 ?
The answer to (e^x+e^{-x})/(e^x+1)=4 is x=ln((sqrt(7)-2)/3)