What is the answer to x^{x^3}=2^{sqrt(2)} ?

The answer to x^{x^3}=2^{sqrt(2)} is x=\sqrt[3]{(sqrt(2)ln(2)*3)/(\W_{0)(3sqrt(2)ln(2))}}

Solve for x: x^{x^3}=2^{sqrt(2)}

The solution is x=\sqrt[3]{(sqrt(2)ln(2)*3)/(\W_{0)(3sqrt(2)ln(2))}}

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x^{x^{3}} = 2^{2}

Solution steps

x^{x^{3}} = 2^{2}

Prepare

x^{x^{3}} = 2^{2}

for Lambert form:

x e^{- \frac{2 l n ( 2 )}{x ^{3}}} = 1

Rewrite the equation with

\frac{2 ln ( 2 )}{x ^{3}} = u

and

Solve

u = \frac{W _{0} ( 3 2 ln ( 2 ) )}{3}

Substitute back

u = \frac{2 ln ( 2 )}{x ^{3}},

solve for

x

Solve

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

k, n = 2^{k}

3^{x} = 19

9^{b^{3} - 1} = 81

e^{4.2 x} = 69

What is the answer to x^{x^3}=2^{sqrt(2)} ?
The answer to x^{x^3}=2^{sqrt(2)} is x=\sqrt[3]{(sqrt(2)ln(2)*3)/(\W_{0)(3sqrt(2)ln(2))}}
Solve for x: x^{x^3}=2^{sqrt(2)}
The solution is x=\sqrt[3]{(sqrt(2)ln(2)*3)/(\W_{0)(3sqrt(2)ln(2))}}