What is the answer to x^{x^5}=5 ?

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

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x^{x^5}=5

x^{x^{5}} = 5

Decimal Notation

x = 1.37972 \dots

Solution steps

x^{x^{5}} = 5

Prepare

x^{x^{5}} = 5

for Lambert form:

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

Rewrite the equation with

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

and

Solve

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

Substitute back

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

solve for

x

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