en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x=e^{2-2x}

Solution

x = e^{2 - 2 x}

Solution

x = 1

Solution steps

x = e^{2 - 2 x}

Prepare

x = e^{2 - 2 x}

for Lambert form:

x e^{- 2 + 2 x} = 1

Rewrite the equation with

2 x = u

and

x = \frac{u}{2}

(\frac{u}{2}) e^{- 2 + 2 (\frac{u}{2})} = 1

Simplify

\frac{e ^{- 2 + u} u}{2} = 1

Rewrite

\frac{e ^{- 2 + u} u}{2} = 1

in Lambert form:

e^{u} u = 2 e^{2}

Solve

e^{u} u = 2 e^{2} : u = 2

u = 2

Substitute back

u = 2 x,

solve for

x

Solve

2 x = 2 : x = 1

x = 1

Popular Examples

2 (3)^{x} = 34

0.5^{0.3x}-8000=20681

0. 5^{0.3 x} - 8000 = 20681

solvefor t,N=3500(2^t)solve for

t, N = 3500 (2^{t})

7+15e^{1-3x}=10

7 + 15 e^{1 - 3 x} = 10

2^{(x + 2)} = 16

Frequently Asked Questions (FAQ)

What is the answer to x=e^{2-2x} ?
The answer to x=e^{2-2x} is x=1