What is the answer to x^{x^{49}}=7^{7^5} ?

The answer to x^{x^{49}}=7^{7^5} is x=\sqrt[49]{(823543ln(7))/(\W_{0)(823543ln(7))}}

Solve for x: x^{x^{49}}=7^{7^5}

The solution is x=\sqrt[49]{(823543ln(7))/(\W_{0)(823543ln(7))}}

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x^{x^{49}} = 7^{7^{5}}

x = 49 \frac{823543 ln ( 7 )}{W _{0} ( 823543 ln ( 7 ) )}

Decimal

x = 1.27274 \dots

Solution steps

x^{x^{49}} = 7^{7^{5}}

Prepare

x^{x^{49}} = 7^{7^{5}}

for Lambert form:

x e^{- \frac{16807 l n ( 7 )}{x ^{49}}} = 1

Rewrite the equation with

\frac{16807 ln ( 7 )}{x ^{49}} = u

and

x = 49 \frac{16807 ln ( 7 )}{u}

49 \frac{16807 ln ( 7 )}{u} e^{- u} = 1

Solve

49 \frac{16807 ln ( 7 )}{u} e^{- u} = 1 : u = \frac{W _{0} ( 823543 ln ( 7 ) )}{49}

u = \frac{W _{0} ( 823543 ln ( 7 ) )}{49}

Substitute back

u = \frac{16807 ln ( 7 )}{x ^{49}},

solve for

x

Solve

\frac{16807 ln ( 7 )}{x ^{49}} = \frac{W _{0} ( 823543 ln ( 7 ) )}{49} : x = 49 \frac{823543 ln ( 7 )}{W _{0} ( 823543 ln ( 7 ) )}

x = 49 \frac{823543 ln ( 7 )}{W _{0} ( 823543 ln ( 7 ) )}

e^{- x} + e^{- 2 x} = \frac{2}{3}

4^{x} - 12 \times 2^{x} + 32 = 0

e^{3 x} - 2 e^{2 x} - 2 e^{x} - 3 = 0

6^{a + 8} - 6 = 73

6 e^{x} = 0

What is the answer to x^{x^{49}}=7^{7^5} ?
The answer to x^{x^{49}}=7^{7^5} is x=\sqrt[49]{(823543ln(7))/(\W_{0)(823543ln(7))}}
Solve for x: x^{x^{49}}=7^{7^5}
The solution is x=\sqrt[49]{(823543ln(7))/(\W_{0)(823543ln(7))}}