What is the answer to x^x=64 ?

The answer to x^x=64 is x=(6ln(2))/(\W_{0)(6ln(2))}

The solution is x=(6ln(2))/(\W_{0)(6ln(2))}

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Popular >

x^x=64

Solution

x^{x} = 64

Solution

x = \frac{6 ln ( 2 )}{W _{0} ( 6 ln ( 2 ) )}

Decimal Notation

x = 3.39912 \dots

Solution steps

x^{x} = 64

Prepare

x^{x} = 64

for Lambert form:

x e^{- \frac{6 l n ( 2 )}{x}} = 1

Rewrite the equation with

\frac{6 ln ( 2 )}{x} = u

and

x = \frac{6 ln ( 2 )}{u}

(\frac{6 ln ( 2 )}{u}) e^{- u} = 1

Rewrite

(\frac{6 ln ( 2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 6 ln (2)

Solve

u e^{u} = 6 ln (2) : u = W_{0} (6 ln (2))

Verify Solutions:

u = W_{0} (6 ln (2))

True

The solution is

u = W_{0} (6 ln (2))

Substitute back

u = \frac{6 ln ( 2 )}{x},

solve for

x

Solve

\frac{6 ln ( 2 )}{x} = W_{0} (6 ln (2)) : x = \frac{6 ln ( 2 )}{W _{0} ( 6 ln ( 2 ) )}

x = \frac{6 ln ( 2 )}{W _{0} ( 6 ln ( 2 ) )}

Popular Examples

e^x(2e^x-1)=10

e^{x} (2 e^{x} - 1) = 10

(1/36)^x=216^{x+5}

(\frac{1}{36})^{x} = 21 6^{x + 5}

2^{x+1}=5^x

2^{x + 1} = 5^{x}

3^x-3^{x-2}=A*3^x

3^{x} - 3^{x - 2} = A \cdot 3^{x}

4^{2x+1}=1

4^{2 x + 1} = 1

Frequently Asked Questions (FAQ)

What is the answer to x^x=64 ?
The answer to x^x=64 is x=(6ln(2))/(\W_{0)(6ln(2))}
Solve for x: x^x=64
The solution is x=(6ln(2))/(\W_{0)(6ln(2))}

x^x=64

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to x^x=64 ?

Solve for x: x^x=64