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Popular >

e^x+3x=0

Solution

e^{x} + 3 x = 0

Solution

x = - W_{0} (\frac{1}{3})

+1

Solution steps

e^{x} + 3 x = 0

Prepare

e^{x} + 3 x = 0

for Lambert form:

1 = - 3 e^{- x} x

Rewrite the equation with

- x = u

and

x = - u

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

Rewrite

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

in Lambert form:

e^{u} u = \frac{1}{3}

Solve

e^{u} u = \frac{1}{3} : u = W_{0} (\frac{1}{3})

u = W_{0} (\frac{1}{3})

Substitute back

u = - x,

solve for

x

Solve

- x = W_{0} (\frac{1}{3}) : x = - W_{0} (\frac{1}{3})

x = - W_{0} (\frac{1}{3})

Popular Examples

5^{n} = 1901

e^{x + 7} = 12

solvefor w,2z=e^w-e^{-w}solve for

w, 2 z = e^{w} - e^{- w}

(60)/(1+e^{-x)}=4

\frac{60}{1 + e ^{- x}} = 4

e^{\frac{k}{12}} = a

Frequently Asked Questions (FAQ)

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