What is the answer to a^a=sqrt(2) ?

The answer to a^a=sqrt(2) is a=(ln(2)}{2\W_{0}(\frac{ln(2))/2)}

Solve for a: a^a=sqrt(2)

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

a^{a} = 2

a = \frac{ln ( 2 )}{2 W _{0} ( \frac{l n ( 2 )}{2} )}

Decimal Notation

a = 1.30435 \dots

Solution steps

a^{a} = 2

Prepare

a^{a} = 2

for Lambert form:

a e^{- \frac{l n ( 2 )}{2 a}} = 1

Rewrite the equation with

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

and

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

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

Rewrite

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

in Lambert form:

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

Solve

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

Verify Solutions:

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

True

The solution is

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

Substitute back

u = \frac{ln ( 2 )}{2 a},

solve for

a

Solve

\frac{ln ( 2 )}{2 a} = W_{0} (\frac{ln ( 2 )}{2}) : a = \frac{ln ( 2 )}{2 W _{0} ( \frac{l n ( 2 )}{2} )}

a = \frac{ln ( 2 )}{2 W _{0} ( \frac{l n ( 2 )}{2} )}

e^{3 x} = 14

x, f = - 2 ((- 6)^{(x + 5)})

e^{3 x} = 22

e^{3 x} = 75

3 = e^{\frac{l n ( 2 )}{50} x}

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