What is the answer to x^x=2^{512} ?

The answer to x^x=2^{512} is x=(512ln(2))/(\W_{0)(512ln(2))}

Solve for x: x^x=2^{512}

The solution is x=(512ln(2))/(\W_{0)(512ln(2))}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{x} = 2^{512}

x = \frac{512 ln ( 2 )}{W _{0} ( 512 ln ( 2 ) )}

Decimal Notation

x = 80.80363 \dots

Solution steps

x^{x} = 2^{512}

Prepare

x^{x} = 2^{512}

for Lambert form:

x e^{- \frac{512 l n ( 2 )}{x}} = 1

Rewrite the equation with

\frac{512 ln ( 2 )}{x} = u

and

x = \frac{512 ln ( 2 )}{u}

(\frac{512 ln ( 2 )}{u}) e^{- u} = 1

Rewrite

(\frac{512 ln ( 2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 512 ln (2)

Solve

u e^{u} = 512 ln (2) : u = W_{0} (512 ln (2))

Verify Solutions:

u = W_{0} (512 ln (2))

True

The solution is

u = W_{0} (512 ln (2))

Substitute back

u = \frac{512 ln ( 2 )}{x},

solve for

x

Solve

\frac{512 ln ( 2 )}{x} = W_{0} (512 ln (2)) : x = \frac{512 ln ( 2 )}{W _{0} ( 512 ln ( 2 ) )}

x = \frac{512 ln ( 2 )}{W _{0} ( 512 ln ( 2 ) )}

5^{x - 1} = 3^{2 x - 1}

x = e^{- x}

6^{x + 1} - 18 \cdot 6^{x - 1} = 108

2^{3 x + 2} = 6

1 0^{x + 2} - 12 = 22

What is the answer to x^x=2^{512} ?
The answer to x^x=2^{512} is x=(512ln(2))/(\W_{0)(512ln(2))}
Solve for x: x^x=2^{512}
The solution is x=(512ln(2))/(\W_{0)(512ln(2))}