What is the answer to x^{x^{49}}=7^{7^6} ?

The answer to x^{x^{49}}=7^{7^6} is x=\sqrt[7]{7}

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x^{x^{49}}=7^{7^6}

x^{x^{49}} = 7^{7^{6}}

Decimal Notation

x = 1.32046 \dots

Solution steps

x^{x^{49}} = 7^{7^{6}}

Prepare

x^{x^{49}} = 7^{7^{6}}

for Lambert form:

x e^{- \frac{117649 l n ( 7 )}{x ^{49}}} = 1

Rewrite the equation with

\frac{117649 ln ( 7 )}{x ^{49}} = u

and

Solve

u = \frac{ln ( 7 )}{7}

Substitute back

u = \frac{117649 ln ( 7 )}{x ^{49}},

solve for

x

Solve

4^{x} = 0.5

x^{\frac{1}{x}} = 2

3^{x} = 47

3^{x} = - 4

2^{x + 1} - 322 = 2^{x}

What is the answer to x^{x^{49}}=7^{7^6} ?
The answer to x^{x^{49}}=7^{7^6} is x=\sqrt[7]{7}
Solve for x: x^{x^{49}}=7^{7^6}
The solution is x=\sqrt[7]{7}