What is the answer to n^n=2 ?

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

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

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Popular >

n^n=2

Solution

n^{n} = 2

Solution

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

Decimal Notation

n = 1.55961 \dots

Solution steps

n^{n} = 2

Prepare

n^{n} = 2

for Lambert form:

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

Rewrite the equation with

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

and

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

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

Rewrite

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

in Lambert form:

u e^{u} = ln (2)

Solve

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

Verify Solutions:

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

True

The solution is

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

Substitute back

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

solve for

n

Solve

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

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

Popular Examples

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e^{x} + 3 e^{- x} = 4

4^{x+1}=16^{x-7}

4^{x + 1} = 1 6^{x - 7}

1000=21(1.2)^t

1000 = 21 (1.2)^{t}

4^x=32

4^{x} = 32

5^{-3}*x+5=0.04^x-3

5^{- 3} \cdot x + 5 = 0.0 4^{x} - 3

Frequently Asked Questions (FAQ)

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

n^n=2

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to n^n=2 ?

Solve for n: n^n=2