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Popular >

x^x=256

Solution

x^{x} = 256

Solution

x = 4

Solution steps

x^{x} = 256

Prepare

x^{x} = 256

for Lambert form:

x e^{- \frac{8 l n ( 2 )}{x}} = 1

Rewrite the equation with

\frac{8 ln ( 2 )}{x} = u

and

x = \frac{8 ln ( 2 )}{u}

(\frac{8 ln ( 2 )}{u}) e^{- u} = 1

Rewrite

(\frac{8 ln ( 2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 8 ln (2)

Solve

u e^{u} = 8 ln (2) : u = 2 ln (2)

Verify Solutions:

u = 2 ln (2)

True

The solution is

u = 2 ln (2)

Substitute back

u = \frac{8 ln ( 2 )}{x},

solve for

x

Solve

\frac{8 ln ( 2 )}{x} = 2 ln (2) : x = 4

x = 4

Popular Examples

e^{3 x} = 2 e^{x}

3^{- x} = 9

4^{x + 1} = 16

e^{x} = 462

e^{- x + 1} = 15

Frequently Asked Questions (FAQ)

What is the answer to x^x=256 ?
The answer to x^x=256 is x=4
Solve for x: x^x=256
The solution is x=4