What is the answer to x^x=65536 ?

The answer to x^x=65536 is x=(16ln(2))/(\W_{0)(16ln(2))}

Solve for x: x^x=65536

The solution is x=(16ln(2))/(\W_{0)(16ln(2))}

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x^{x} = 65536

x = \frac{16 ln ( 2 )}{W _{0} ( 16 ln ( 2 ) )}

Decimal Notation

x = 6.12127 \dots

Solution steps

x^{x} = 65536

Prepare

x^{x} = 65536

for Lambert form:

x e^{- \frac{16 l n ( 2 )}{x}} = 1

Rewrite the equation with

\frac{16 ln ( 2 )}{x} = u

and

x = \frac{16 ln ( 2 )}{u}

(\frac{16 ln ( 2 )}{u}) e^{- u} = 1

Rewrite

(\frac{16 ln ( 2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 16 ln (2)

Solve

u e^{u} = 16 ln (2) : u = W_{0} (16 ln (2))

Verify Solutions:

u = W_{0} (16 ln (2))

True

The solution is

u = W_{0} (16 ln (2))

Substitute back

u = \frac{16 ln ( 2 )}{x},

solve for

x

Solve

\frac{16 ln ( 2 )}{x} = W_{0} (16 ln (2)) : x = \frac{16 ln ( 2 )}{W _{0} ( 16 ln ( 2 ) )}

x = \frac{16 ln ( 2 )}{W _{0} ( 16 ln ( 2 ) )}

x, y^{\cdot} + 9 y = e^{2 x} 7

2^{x - 4} = 4^{x - 6}

2 x = 8^{x} + 4

3^{- 4 x} = 9^{6 - x}

4^{2 n + 1} - 12 = 52

What is the answer to x^x=65536 ?
The answer to x^x=65536 is x=(16ln(2))/(\W_{0)(16ln(2))}
Solve for x: x^x=65536
The solution is x=(16ln(2))/(\W_{0)(16ln(2))}