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

Solve

e^{3 x} = 2 + x

e^{2 t + 1} = 9 e^{1 - t}

x - 3^{- x} = 0

4^{x} + 6^{x} = 2 \cdot 9^{x}

2^{x^{2} + x} = 4^{x + 1}