What is the answer to e^x-6x=0 ?

The answer to e^x-6x=0 is x=-\W_{-1}(-1/6),x=-\W_{0}(-1/6)

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e^x-6x=0

e^{x} - 6 x = 0

x = - W_{- 1} (- \frac{1}{6}), x = - W_{0} (- \frac{1}{6})

Decimal Notation

x = 2.83314 \dots, x = 0.20448 \dots

Solution steps

e^{x} - 6 x = 0

Prepare

e^{x} - 6 x = 0

for Lambert form:

1 = 6 x e^{- x}

Rewrite the equation with

- x = u

and

x = - u

1 = 6 (- u) e^{u}

Rewrite

1 = 6 (- u) e^{u}

in Lambert form:

e^{u} u = - \frac{1}{6}

Solve

e^{u} u = - \frac{1}{6} : u = W_{- 1} (- \frac{1}{6}), u = W_{0} (- \frac{1}{6})

u = W_{- 1} (- \frac{1}{6}), u = W_{0} (- \frac{1}{6})

Substitute back

u = - x,

solve for

x

Solve

- x = W_{- 1} (- \frac{1}{6}) : x = - W_{- 1} (- \frac{1}{6})

Solve

- x = W_{0} (- \frac{1}{6}) : x = - W_{0} (- \frac{1}{6})

x = - W_{- 1} (- \frac{1}{6}), x = - W_{0} (- \frac{1}{6})

3 e^{x} - 4 x e^{x} = 0

3 \cdot 1 0^{- 9} = 1 0^{- x}

- e^{x + 4} = - 58

3^{n} = 3 \cdot 9^{3} \cdot 8 1^{2}

e^{a} = a

What is the answer to e^x-6x=0 ?
The answer to e^x-6x=0 is x=-\W_{-1}(-1/6),x=-\W_{0}(-1/6)