What is the answer to x^x=6 ?

The answer to x^x=6 is x=(ln(6))/(\W_{0)(ln(6))}

The solution is x=(ln(6))/(\W_{0)(ln(6))}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^x=6

Solution

x^{x} = 6

Solution

x = \frac{ln ( 6 )}{W _{0} ( ln ( 6 ) )}

Decimal Notation

x = 2.23182 \dots

Solution steps

x^{x} = 6

Prepare

x^{x} = 6

for Lambert form:

x e^{- \frac{l n ( 6 )}{x}} = 1

Rewrite the equation with

\frac{ln ( 6 )}{x} = u

and

x = \frac{ln ( 6 )}{u}

(\frac{ln ( 6 )}{u}) e^{- u} = 1

Rewrite

(\frac{ln ( 6 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = ln (6)

Solve

u e^{u} = ln (6) : u = W_{0} (ln (6))

Verify Solutions:

u = W_{0} (ln (6))

True

The solution is

u = W_{0} (ln (6))

Substitute back

u = \frac{ln ( 6 )}{x},

solve for

x

Solve

\frac{ln ( 6 )}{x} = W_{0} (ln (6)) : x = \frac{ln ( 6 )}{W _{0} ( ln ( 6 ) )}

x = \frac{ln ( 6 )}{W _{0} ( ln ( 6 ) )}

Popular Examples

3^{3x+5}=3*9^{x+3}

3^{3 x + 5} = 3 \cdot 9^{x + 3}

9^x-10\times 3^x+9=0

9^{x} - 10 \times 3^{x} + 9 = 0

5^{a+2}= 1/125

5^{a + 2} = \frac{1}{125}

solvefor x,y=12^{1-0.1x}solve for

x, y = 1 2^{1 - 0.1 x}

(1-x)/(e^x)=0

\frac{1 - x}{e ^{x}} = 0

Frequently Asked Questions (FAQ)

What is the answer to x^x=6 ?
The answer to x^x=6 is x=(ln(6))/(\W_{0)(ln(6))}
Solve for x: x^x=6
The solution is x=(ln(6))/(\W_{0)(ln(6))}

x^x=6

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to x^x=6 ?

Solve for x: x^x=6