What is the answer to e^x+e^{-x}=9 ?

The answer to e^x+e^{-x}=9 is x=ln((9+sqrt(77))/2),x=ln((9-sqrt(77))/2)

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e^x+e^{-x}=9

e^{x} + e^{- x} = 9

x = ln (\frac{9 + 77}{2}), x = ln (\frac{9 - 77}{2})

Decimal Notation

x = 2.18464 \dots, x = - 2.18464 \dots

Solution steps

e^{x} + e^{- x} = 9

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 9

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 9

Solve

u + u^{- 1} = 9 : u = \frac{9 + 77}{2}, u = \frac{9 - 77}{2}

u = \frac{9 + 77}{2}, u = \frac{9 - 77}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{9 + 77}{2} : x = ln (\frac{9 + 77}{2})

Solve

e^{x} = \frac{9 - 77}{2} : x = ln (\frac{9 - 77}{2})

x = ln (\frac{9 + 77}{2}), x = ln (\frac{9 - 77}{2})

4 \cdot 3^{x - 2} = 60

3^{x} = \frac{1}{27}

2 0^{b} = 4

1240000 = 525600 e^{0.03 (t)}

e^{l n (x + 1)} = 3

What is the answer to e^x+e^{-x}=9 ?
The answer to e^x+e^{-x}=9 is x=ln((9+sqrt(77))/2),x=ln((9-sqrt(77))/2)