What is the answer to x^{x^5}=\sqrt[5]{4} ?

The answer to x^{x^5}=\sqrt[5]{4} is x=\sqrt[5]{2}

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x^{x^5}=\sqrt[5]{4}

Solution steps

Prepare

for Lambert form:

x e^{- \frac{2 l n ( 2 )}{5 x ^{5}}} = 1

Rewrite the equation with

\frac{2 ln ( 2 )}{5 x ^{5}} = u

and

Solve

u = \frac{ln ( 2 )}{5}

Substitute back

u = \frac{2 ln ( 2 )}{5 x ^{5}},

solve for

x

Solve

5^{2 x} = 42

5^{2 x} = 25

3 = 1.1 2^{x}

4^{2 v} = 64

e^{x} e^{2 x} = 4

What is the answer to x^{x^5}=\sqrt[5]{4} ?
The answer to x^{x^5}=\sqrt[5]{4} is x=\sqrt[5]{2}
Solve for x: x^{x^5}=\sqrt[5]{4}
The solution is x=\sqrt[5]{2}