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Popular >

e^x=-3x

Solution

e^{x} = - 3 x

Solution

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

+1

Decimal

x = - 0.25762 \dots

Solution steps

e^{x} = - 3 x

Prepare

e^{x} = - 3 x

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})

Graph

Popular Examples

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4^{2 x} = \frac{1}{2 ^{3}}

7^a=\sqrt[8]{7}

7^{a} = 87

e^{x} + 2 = 0

4^{x} = 9^{x - 2}

10 e - 0.0 3^{t} = 4

Frequently Asked Questions (FAQ)

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