What is the answer to e^{(-2x)}-2e^{-x}=-0.5 ?

The answer to e^{(-2x)}-2e^{-x}=-0.5 is x=ln(2-sqrt(2)),x=ln(2+sqrt(2))

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e^{(-2x)}-2e^{-x}=-0.5

e^{(- 2 x)} - 2 e^{- x} = - 0.5

x = ln (2 - 2), x = ln (2 + 2)

Solution steps

e^{(- 2 x)} - 2 e^{- x} = - 0.5

Apply exponent rules

(e^{x})^{- 2} - 2 (e^{x})^{- 1} = - 0.5

Rewrite the equation with

e^{x} = u

(u)^{- 2} - 2 (u)^{- 1} = - 0.5

Solve

u^{- 2} - 2 u^{- 1} = - 0.5 : u = 2 - 2, u = 2 + 2

u = 2 - 2, u = 2 + 2

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

x = ln (2 - 2), x = ln (2 + 2)

e^{5 x} = 7800

x, e^{x + y} = 0

x, e^{x + y} = 1

n, s = \frac{a ^{n}}{b}

6 \cdot 5^{3 x} = 468750

What is the answer to e^{(-2x)}-2e^{-x}=-0.5 ?
The answer to e^{(-2x)}-2e^{-x}=-0.5 is x=ln(2-sqrt(2)),x=ln(2+sqrt(2))