What is the answer to e^x-5x=0 ?

The answer to e^x-5x=0 is x=-\W_{-1}(-1/5),x=-\W_{0}(-1/5)

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e^x-5x=0

e^{x} - 5 x = 0

x = - W_{- 1} (- \frac{1}{5}), x = - W_{0} (- \frac{1}{5})

Decimal Notation

x = 2.54264 \dots, x = 0.25917 \dots

Solution steps

e^{x} - 5 x = 0

Prepare

e^{x} - 5 x = 0

for Lambert form:

1 = 5 x e^{- x}

Rewrite the equation with

- x = u

and

x = - u

1 = 5 (- u) e^{u}

Rewrite

1 = 5 (- u) e^{u}

in Lambert form:

e^{u} u = - \frac{1}{5}

Solve

e^{u} u = - \frac{1}{5} : u = W_{- 1} (- \frac{1}{5}), u = W_{0} (- \frac{1}{5})

u = W_{- 1} (- \frac{1}{5}), u = W_{0} (- \frac{1}{5})

Substitute back

u = - x,

solve for

x

Solve

- x = W_{- 1} (- \frac{1}{5}) : x = - W_{- 1} (- \frac{1}{5})

Solve

- x = W_{0} (- \frac{1}{5}) : x = - W_{0} (- \frac{1}{5})

x = - W_{- 1} (- \frac{1}{5}), x = - W_{0} (- \frac{1}{5})

ln (3) \cdot 3^{x} = 0

2^{5 x} = 16

(- 3)^{x} = - 27

4^{2 x^{2}} = \frac{1}{1 6 ^{3 x - 1}}

2^{x} \cdot 4^{2 - x} = 8

What is the answer to e^x-5x=0 ?
The answer to e^x-5x=0 is x=-\W_{-1}(-1/5),x=-\W_{0}(-1/5)