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(6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = ln (- 2 + 6)

Decimal Notation

x = - 0.79964 \dots

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 + 6, u = - 2 - 6

u = - 2 + 6, u = - 2 - 6

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = - 2 + 6 : x = ln (- 2 + 6)

Solve

e^{x} = - 2 - 6 :

No Solution for

x \in R

x = ln (- 2 + 6)

x, 2 = e^{x}

5^{(- 3 x + 6)} = 5^{(8 x + 3)}

2 (1 0^{6}) = 1 0^{6} e^{12 k}

8^{x} + 8^{x} = 2^{100}

64000 = \frac{1}{80} e^{x (210)}

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(6))