What is the answer to x^x=31 ?

The answer to x^x=31 is x=(ln(31))/(\W_{0)(ln(31))}

The solution is x=(ln(31))/(\W_{0)(ln(31))}

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Popular >

x^x=31

Solution

x^{x} = 31

Solution

x = \frac{ln ( 31 )}{W _{0} ( ln ( 31 ) )}

Decimal Notation

x = 3.06549 \dots

Solution steps

x^{x} = 31

Prepare

x^{x} = 31

for Lambert form:

x e^{- \frac{l n ( 31 )}{x}} = 1

Rewrite the equation with

\frac{ln ( 31 )}{x} = u

and

x = \frac{ln ( 31 )}{u}

(\frac{ln ( 31 )}{u}) e^{- u} = 1

Rewrite

(\frac{ln ( 31 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = ln (31)

Solve

u e^{u} = ln (31) : u = W_{0} (ln (31))

Verify Solutions:

u = W_{0} (ln (31))

True

The solution is

u = W_{0} (ln (31))

Substitute back

u = \frac{ln ( 31 )}{x},

solve for

x

Solve

\frac{ln ( 31 )}{x} = W_{0} (ln (31)) : x = \frac{ln ( 31 )}{W _{0} ( ln ( 31 ) )}

x = \frac{ln ( 31 )}{W _{0} ( ln ( 31 ) )}

Popular Examples

2^{3x-1}-2^{2x-1}=2^{x+3}-2

2^{3 x - 1} - 2^{2 x - 1} = 2^{x + 3} - 2

e^{3x}= 1/8

e^{3 x} = \frac{1}{8}

3(4^x)=(2)^{3x-5}

3 (4^{x}) = (2)^{3 x - 5}

0.5^{(9900)/x}=30

0. 5^{\frac{9900}{x}} = 30

3*5^{(x+1)}=7*4^x

3 \cdot 5^{(x + 1)} = 7 \cdot 4^{x}

Frequently Asked Questions (FAQ)

What is the answer to x^x=31 ?
The answer to x^x=31 is x=(ln(31))/(\W_{0)(ln(31))}
Solve for x: x^x=31
The solution is x=(ln(31))/(\W_{0)(ln(31))}

x^x=31

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to x^x=31 ?

Solve for x: x^x=31