What is the answer to (\sqrt[3]{x})/(e^x)+1=0 ?

The answer to (\sqrt[3]{x})/(e^x)+1=0 is x=-(\W_{0}(3))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\sqrt[3]{x})/(e^x)+1=0

x = - \frac{W _{0} ( 3 )}{3}

Decimal Notation

x = - 0.34996 \dots

Solution steps

Prepare

for Lambert form:

e^{- 3 x} x = - 1

Rewrite the equation with

- 3 x = u

and

x = - \frac{u}{3}

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

Rewrite

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

in Lambert form:

e^{u} u = 3

Solve

e^{u} u = 3 : u = W_{0} (3)

u = W_{0} (3)

Substitute back

u = - 3 x,

solve for

x

Solve

- 3 x = W_{0} (3) : x = - \frac{W _{0} ( 3 )}{3}

x = - \frac{W _{0} ( 3 )}{3}

Verify Solutions:

x = - \frac{W _{0} ( 3 )}{3}

True

The solution is

x = - \frac{W _{0} ( 3 )}{3}

Verify Solutions:

x = - \frac{W _{0} ( 3 )}{3}

True

The solution is

x = - \frac{W _{0} ( 3 )}{3}

1000 = 300 + 200 e^{0.2 t}

e^{3 k} = 64

\frac{1000}{27} = (1312)^{t}

6 \cdot e^{0.25 x} = 9

2 7^{x} = 8 1^{1 - x}

What is the answer to (\sqrt[3]{x})/(e^x)+1=0 ?
The answer to (\sqrt[3]{x})/(e^x)+1=0 is x=-(\W_{0}(3))/3