What is the answer to -(ln(1-x))/x =1.5 ?

The answer to -(ln(1-x))/x =1.5 is x=(2\W_{0}(-3/(2e^{3/2)})+3)/3

Solve for x: -(ln(1-x))/x =1.5

The solution is x=(2\W_{0}(-3/(2e^{3/2)})+3)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

- \frac{ln ( 1 - x )}{x} = 1.5

x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

Decimal Notation

x = 0.58281 \dots

Solution steps

- \frac{ln ( 1 - x )}{x} = 1.5

Multiply both sides by

x

- ln (1 - x) = 1.5 x

Multiply both sides by

10

- ln (1 - x) \cdot 10 = 15 x

Divide both sides by

- 10

ln (1 - x) = - \frac{3 x}{2}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (1 - x)} = e^{- \frac{3 x}{2}}

Simplify

e^{l n (1 - x)} : 1 - x

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

Solve

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

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

Verify Solutions:

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

False

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

True

The solution is

x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

lo g_{5} (2 x - 3) = 3

lo g_{10} (x + 9) - lo g_{10} (x) = 1

lo g_{4} (x) + lo g_{2} (x) = 6

lo g_{2} (3 x - 4) = 5

lo g_{x} (64) = \frac{3}{2}

What is the answer to -(ln(1-x))/x =1.5 ?
The answer to -(ln(1-x))/x =1.5 is x=(2\W_{0}(-3/(2e^{3/2)})+3)/3
Solve for x: -(ln(1-x))/x =1.5
The solution is x=(2\W_{0}(-3/(2e^{3/2)})+3)/3