What is the answer to x=(1/2)^x ?

The answer to x=(1/2)^x is x=(\W_{0}(ln(2)))/(ln(2))

Solve for x: x=(1/2)^x

The solution is x=(\W_{0}(ln(2)))/(ln(2))

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x = (\frac{1}{2})^{x}

x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

Decimal Notation

x = 0.64118 \dots

Solution steps

x = (\frac{1}{2})^{x}

Prepare

x = (\frac{1}{2})^{x}

for Lambert form:

x e^{l n (2) x} = 1

Rewrite the equation with

ln (2) x = u

and

x = \frac{u}{ln ( 2 )}

(\frac{u}{ln ( 2 )}) e^{u} = 1

Rewrite

(\frac{u}{ln ( 2 )}) e^{u} = 1

in Lambert form:

e^{u} u = ln (2)

Solve

e^{u} u = ln (2) : u = W_{0} (ln (2))

u = W_{0} (ln (2))

Substitute back

u = ln (2) x,

solve for

x

Solve

ln (2) x = W_{0} (ln (2)) : x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

2^{x} = 1.3

(\frac{1}{5})^{3 x - 2} = 62 5^{8}

\frac{4000}{2000} = 1.2 5^{n}

(\frac{7}{5})^{x - 1} = (\frac{5}{7})^{x - 3}

y, x^{4} - 2 x^{y} - 1 = 0

What is the answer to x=(1/2)^x ?
The answer to x=(1/2)^x is x=(\W_{0}(ln(2)))/(ln(2))
Solve for x: x=(1/2)^x
The solution is x=(\W_{0}(ln(2)))/(ln(2))