What is the answer to a^a=2 ?

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

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

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Popular >

a^a=2

Solution

a^{a} = 2

Solution

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

Decimal Notation

a = 1.55961 \dots

Solution steps

a^{a} = 2

Prepare

a^{a} = 2

for Lambert form:

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

Rewrite the equation with

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

and

a = \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 )}{a},

solve for

a

Solve

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

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

Popular Examples

1800=900(1+0.06)^X

1800 = 900 (1 + 0.06)^{X}

8=3(5)^x

8 = 3 (5)^{x}

solvefor t,x=e^{-3t}solve for

t, x = e^{- 3 t}

4^x+9*2^x+23=0

4^{x} + 9 \cdot 2^{x} + 23 = 0

(2^{x+2})/(16)=sqrt(2)

\frac{2 ^{x + 2}}{16} = 2

Frequently Asked Questions (FAQ)

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

a^a=2

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to a^a=2 ?

Solve for a: a^a=2