What is the answer to x^{x^7}=\sqrt[14]{2} ?

The answer to x^{x^7}=\sqrt[14]{2} is x=\sqrt[7]{(ln(2)}{2\W_{0}(\frac{ln(2))/2)}}

Solve for x: x^{x^7}=\sqrt[14]{2}

The solution is x=\sqrt[7]{(ln(2)}{2\W_{0}(\frac{ln(2))/2)}}

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Decimal Notation

x = 1.03868 \dots

Solution steps

Prepare

for Lambert form:

x e^{- \frac{l n ( 2 )}{14 x ^{7}}} = 1

Rewrite the equation with

\frac{ln ( 2 )}{14 x ^{7}} = u

and

Solve

u = \frac{W _{0} ( \frac{l n ( 2 )}{2} )}{7}

Substitute back

u = \frac{ln ( 2 )}{14 x ^{7}},

solve for

x

Solve

e^{3 x} = \frac{1}{16}

2^{n + 1} = \frac{1}{16}

e^{7 + 2 x} - 3 = 0

(\frac{1}{8})^{2 x + 1} = 64

75 e^{x} = 42

What is the answer to x^{x^7}=\sqrt[14]{2} ?
The answer to x^{x^7}=\sqrt[14]{2} is x=\sqrt[7]{(ln(2)}{2\W_{0}(\frac{ln(2))/2)}}
Solve for x: x^{x^7}=\sqrt[14]{2}
The solution is x=\sqrt[7]{(ln(2)}{2\W_{0}(\frac{ln(2))/2)}}