What is the answer to x^x=10^{36*10^9} ?

The answer to x^x=10^{36*10^9} is x=(36000000000ln(10))/(\W_{0)(36000000000ln(10))}

Solve for x: x^x=10^{36*10^9}

The solution is x=(36000000000ln(10))/(\W_{0)(36000000000ln(10))}

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x^{x} = 1 0^{36 \cdot 1 0^{9}}

x = \frac{36000000000 ln ( 10 )}{W _{0} ( 36000000000 ln ( 10 ) )}

Solution steps

x^{x} = 1 0^{36 \cdot 1 0^{9}}

Prepare

x^{x} = 1 0^{36 \cdot 1 0^{9}}

for Lambert form:

x e^{- \frac{36000000000 l n ( 10 )}{x}} = 1

Rewrite the equation with

\frac{36000000000 ln ( 10 )}{x} = u

and

x = \frac{36000000000 ln ( 10 )}{u}

(\frac{36000000000 ln ( 10 )}{u}) e^{- u} = 1

Rewrite

(\frac{36000000000 ln ( 10 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = 36000000000 ln (10)

Solve

u e^{u} = 36000000000 ln (10) : u = W_{0} (36000000000 ln (10))

Verify Solutions:

u = W_{0} (36000000000 ln (10))

True

The solution is

u = W_{0} (36000000000 ln (10))

Substitute back

u = \frac{36000000000 ln ( 10 )}{x},

solve for

x

Solve

\frac{36000000000 ln ( 10 )}{x} = W_{0} (36000000000 ln (10)) : x = \frac{36000000000 ln ( 10 )}{W _{0} ( 36000000000 ln ( 10 ) )}

x = \frac{36000000000 ln ( 10 )}{W _{0} ( 36000000000 ln ( 10 ) )}

k, k^{2} t^{k} = 0

2 e^{(x + 6)} = 20

f, e^{f} = x

x, c^{x + 3} - c^{8} = 0

What is the answer to x^x=10^{36*10^9} ?
The answer to x^x=10^{36*10^9} is x=(36000000000ln(10))/(\W_{0)(36000000000ln(10))}
Solve for x: x^x=10^{36*10^9}
The solution is x=(36000000000ln(10))/(\W_{0)(36000000000ln(10))}