What is the answer to X^{X^3}=3 ?

The answer to X^{X^3}=3 is X=\sqrt[3]{3}

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X^{X^3}=3

X^{X^{3}} = 3

Decimal Notation

X = 1.44224 \dots

Solution steps

X^{X^{3}} = 3

Prepare

X^{X^{3}} = 3

for Lambert form:

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

Rewrite the equation with

\frac{ln ( 3 )}{X ^{3}} = u

and

Solve

u = \frac{ln ( 3 )}{3}

Substitute back

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

solve for

X

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