What is the answer to x^x=3 ?

The answer to x^x=3 is x=(ln(3))/(\W_{0)(ln(3))}

The solution is x=(ln(3))/(\W_{0)(ln(3))}

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Popular >

x^x=3

Solution

x^{x} = 3

Solution

x = \frac{ln ( 3 )}{W _{0} ( ln ( 3 ) )}

Decimal Notation

x = 1.82545 \dots

Solution steps

x^{x} = 3

Prepare

x^{x} = 3

for Lambert form:

x e^{- \frac{l n ( 3 )}{x}} = 1

Rewrite the equation with

\frac{ln ( 3 )}{x} = u

and

x = \frac{ln ( 3 )}{u}

(\frac{ln ( 3 )}{u}) e^{- u} = 1

Rewrite

(\frac{ln ( 3 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = ln (3)

Solve

u e^{u} = ln (3) : u = W_{0} (ln (3))

Verify Solutions:

u = W_{0} (ln (3))

True

The solution is

u = W_{0} (ln (3))

Substitute back

u = \frac{ln ( 3 )}{x},

solve for

x

Solve

\frac{ln ( 3 )}{x} = W_{0} (ln (3)) : x = \frac{ln ( 3 )}{W _{0} ( ln ( 3 ) )}

x = \frac{ln ( 3 )}{W _{0} ( ln ( 3 ) )}

Popular Examples

5^x=3

5^{x} = 3

25^{x-1}=5^{2x-1}-100

2 5^{x - 1} = 5^{2 x - 1} - 100

64^{x-2}=256^{2x}

6 4^{x - 2} = 25 6^{2 x}

5^x=125

5^{x} = 125

((2/3)^x*1)/(((2/3)^4))=1

\frac{( \frac{2}{3} ) ^{x} \cdot 1}{( ( \frac{2}{3} ) ^{4} )} = 1

Frequently Asked Questions (FAQ)

What is the answer to x^x=3 ?
The answer to x^x=3 is x=(ln(3))/(\W_{0)(ln(3))}
Solve for x: x^x=3
The solution is x=(ln(3))/(\W_{0)(ln(3))}

x^x=3

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to x^x=3 ?

Solve for x: x^x=3