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Popular >

x^x=2^{24}

Solution

x^{x} = 2^{24}

Solution

x = 8

Solution steps

x^{x} = 2^{24}

Prepare

x^{x} = 2^{24}

for Lambert form:

x e^{- \frac{24 l n ( 2 )}{x}} = 1

Rewrite the equation with

\frac{24 ln ( 2 )}{x} = u

and

x = \frac{24 ln ( 2 )}{u}

(\frac{24 ln ( 2 )}{u}) e^{- u} = 1

Rewrite

(\frac{24 ln ( 2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 24 ln (2)

Solve

u e^{u} = 24 ln (2) : u = 3 ln (2)

Verify Solutions:

u = 3 ln (2)

True

The solution is

u = 3 ln (2)

Substitute back

u = \frac{24 ln ( 2 )}{x},

solve for

x

Solve

\frac{24 ln ( 2 )}{x} = 3 ln (2) : x = 8

x = 8

Popular Examples

solvefor x,y*e^x=1 solve for

x, y \cdot e^{x} = 1

3 \cdot 3^{x} = 12

x^{x^7}=\sqrt[14]{2}

e^{3 x} = \frac{1}{16}

2^{n + 1} = \frac{1}{16}

Frequently Asked Questions (FAQ)

What is the answer to x^x=2^{24} ?
The answer to x^x=2^{24} is x=8
Solve for x: x^x=2^{24}
The solution is x=8