What is the answer to x^x=16 ?

The answer to x^x=16 is x=(4ln(2))/(\W_{0)(4ln(2))}

The solution is x=(4ln(2))/(\W_{0)(4ln(2))}

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Popular >

x^x=16

Solution

x^{x} = 16

Solution

x = \frac{4 ln ( 2 )}{W _{0} ( 4 ln ( 2 ) )}

Decimal Notation

x = 2.74536 \dots

Solution steps

x^{x} = 16

Prepare

x^{x} = 16

for Lambert form:

x e^{- \frac{4 l n ( 2 )}{x}} = 1

Rewrite the equation with

\frac{4 ln ( 2 )}{x} = u

and

x = \frac{4 ln ( 2 )}{u}

(\frac{4 ln ( 2 )}{u}) e^{- u} = 1

Rewrite

(\frac{4 ln ( 2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 4 ln (2)

Solve

u e^{u} = 4 ln (2) : u = W_{0} (4 ln (2))

Verify Solutions:

u = W_{0} (4 ln (2))

True

The solution is

u = W_{0} (4 ln (2))

Substitute back

u = \frac{4 ln ( 2 )}{x},

solve for

x

Solve

\frac{4 ln ( 2 )}{x} = W_{0} (4 ln (2)) : x = \frac{4 ln ( 2 )}{W _{0} ( 4 ln ( 2 ) )}

x = \frac{4 ln ( 2 )}{W _{0} ( 4 ln ( 2 ) )}

Popular Examples

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

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

5^{1-x}=2^x

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

36^3=6^{x-1}

3 6^{3} = 6^{x - 1}

solvefor x, J/e =Je^{-xy}solve for

x, \frac{J}{e} = J e^{- x y}

7^x+7^{1-x}=8

7^{x} + 7^{1 - x} = 8

Frequently Asked Questions (FAQ)

What is the answer to x^x=16 ?
The answer to x^x=16 is x=(4ln(2))/(\W_{0)(4ln(2))}
Solve for x: x^x=16
The solution is x=(4ln(2))/(\W_{0)(4ln(2))}

x^x=16

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to x^x=16 ?

Solve for x: x^x=16