What is the answer to e^{1-3x}=3-2x ?

The answer to e^{1-3x}=3-2x is x=(2\W_{-1}(-3/(2e^{7/2)})+9)/6 ,x=(2\W_{0}(-3/(2e^{7/2)})+9)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^{1-3x}=3-2x

e^{1 - 3 x} = 3 - 2 x

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{7}{2}}} ) + 9}{6}, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{7}{2}}} ) + 9}{6}

Decimal Notation

x = - 0.04209 \dots, x = 1.48416 \dots

Solution steps

e^{1 - 3 x} = 3 - 2 x

Prepare

e^{1 - 3 x} = 3 - 2 x

for Lambert form:

1 = (3 - 2 x) e^{- 1 + 3 x}

Rewrite the equation with

3 x - \frac{9}{2} = u

and

x = \frac{2 u + 9}{6}

1 = (3 - 2 (\frac{2 u + 9}{6})) e^{- 1 + 3 (\frac{2 u + 9}{6})}

Simplify

1 = e^{- 1 + \frac{2 u + 9}{2}} (3 - \frac{2 u + 9}{3})

Rewrite

1 = e^{- 1 + \frac{2 u + 9}{2}} (3 - \frac{2 u + 9}{3})

in Lambert form:

e^{u} u = - \frac{3}{2 e ^{\frac{7}{2}}}

Solve

e^{u} u = - \frac{3}{2 e ^{\frac{7}{2}}} : u = W_{- 1} (- \frac{3}{2 e ^{\frac{7}{2}}}), u = W_{0} (- \frac{3}{2 e ^{\frac{7}{2}}})

u = W_{- 1} (- \frac{3}{2 e ^{\frac{7}{2}}}), u = W_{0} (- \frac{3}{2 e ^{\frac{7}{2}}})

Substitute back

u = 3 x - \frac{9}{2},

solve for

x

Solve

3 x - \frac{9}{2} = W_{- 1} (- \frac{3}{2 e ^{\frac{7}{2}}}) : x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{7}{2}}} ) + 9}{6}

Solve

3 x - \frac{9}{2} = W_{0} (- \frac{3}{2 e ^{\frac{7}{2}}}) : x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{7}{2}}} ) + 9}{6}

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{7}{2}}} ) + 9}{6}, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{7}{2}}} ) + 9}{6}

2^{x} = - 8

2^{x} = - 5

2^{x} = - 7

2^{x} = 25

2^{x} = 23

What is the answer to e^{1-3x}=3-2x ?
The answer to e^{1-3x}=3-2x is x=(2\W_{-1}(-3/(2e^{7/2)})+9)/6 ,x=(2\W_{0}(-3/(2e^{7/2)})+9)/6