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Popular >

x^x=4

Solution

x^{x} = 4

Solution

x = 2

Solution steps

x^{x} = 4

Prepare

x^{x} = 4

for Lambert form:

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

Rewrite the equation with

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

and

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

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

Rewrite

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

in Lambert form:

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

Solve

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

Verify Solutions:

u = ln (2)

True

The solution is

u = ln (2)

Substitute back

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

solve for

x

Solve

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

x = 2

Popular Examples

x^{x} = 5

(a)log_{3}(1+log_{3}(2^x-7))=1

(a) lo g_{3} (1 + lo g_{3} (2^{x} - 7)) = 1

2^{x - 3} = 128

(7^{x+1})^{1/5}=7

(7^{x + 1})^{\frac{1}{5}} = 7

2^{x} + 1 + 2^{x} + 2 = 48

Frequently Asked Questions (FAQ)

What is the answer to x^x=4 ?
The answer to x^x=4 is x=2
Solve for x: x^x=4
The solution is x=2