What is the answer to e^{3-2x}=8-3x ?

The answer to e^{3-2x}=8-3x is x=(3\W_{-1}(-2/(3e^{7/3)})+16)/6 ,x=(3\W_{0}(-2/(3e^{7/3)})+16)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^{3-2x}=8-3x

e^{3 - 2 x} = 8 - 3 x

x = \frac{3 W _{- 1} ( - \frac{2}{3 e ^{\frac{7}{3}}} ) + 16}{6}, x = \frac{3 W _{0} ( - \frac{2}{3 e ^{\frac{7}{3}}} ) + 16}{6}

Decimal Notation

x = 0.58382 \dots, x = 2.63202 \dots

Solution steps

e^{3 - 2 x} = 8 - 3 x

Prepare

e^{3 - 2 x} = 8 - 3 x

for Lambert form:

1 = (8 - 3 x) e^{- 3 + 2 x}

Rewrite the equation with

2 x - \frac{16}{3} = u

and

x = \frac{3 u + 16}{6}

1 = (8 - 3 (\frac{3 u + 16}{6})) e^{- 3 + 2 (\frac{3 u + 16}{6})}

Simplify

1 = e^{- 3 + \frac{3 u + 16}{3}} (8 - \frac{3 u + 16}{2})

Rewrite

1 = e^{- 3 + \frac{3 u + 16}{3}} (8 - \frac{3 u + 16}{2})

in Lambert form:

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

Solve

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

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

Substitute back

u = 2 x - \frac{16}{3},

solve for

x

Solve

2 x - \frac{16}{3} = W_{- 1} (- \frac{2}{3 e ^{\frac{7}{3}}}) : x = \frac{3 W _{- 1} ( - \frac{2}{3 e ^{\frac{7}{3}}} ) + 16}{6}

Solve

2 x - \frac{16}{3} = W_{0} (- \frac{2}{3 e ^{\frac{7}{3}}}) : x = \frac{3 W _{0} ( - \frac{2}{3 e ^{\frac{7}{3}}} ) + 16}{6}

x = \frac{3 W _{- 1} ( - \frac{2}{3 e ^{\frac{7}{3}}} ) + 16}{6}, x = \frac{3 W _{0} ( - \frac{2}{3 e ^{\frac{7}{3}}} ) + 16}{6}

2^{4 x + 3} = 512

a, ln (x^{(2 - a)}) = 4

3^{n} = 81

4^{x + 2} = 1 6^{2 x - 4}

5^{- 2 x + 1} = 2 5^{x - 2}

What is the answer to e^{3-2x}=8-3x ?
The answer to e^{3-2x}=8-3x is x=(3\W_{-1}(-2/(3e^{7/3)})+16)/6 ,x=(3\W_{0}(-2/(3e^{7/3)})+16)/6