What is the answer to \sqrt[x]{x}=sqrt(0.5) ?

The answer to \sqrt[x]{x}=sqrt(0.5) is x=-(2\W_{0}(-(ln(0.5))/2))/(ln(0.5))

Solve for x: \sqrt[x]{x}=sqrt(0.5)

The solution is x=-(2\W_{0}(-(ln(0.5))/2))/(ln(0.5))

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x = - \frac{2 W _{0} ( - \frac{l n ( 0.5 )}{2} )}{ln ( 0.5 )}

Decimal Notation

x = 0.76666 \dots

Solution steps

Apply exponent rules

\frac{1}{x} ln (x) = \frac{1}{2} ln (0.5)

Solve

\frac{1}{x} ln (x) = \frac{1}{2} ln (0.5) : x = - \frac{2 W _{0} ( - \frac{l n ( 0.5 )}{2} )}{ln ( 0.5 )}

x = - \frac{2 W _{0} ( - \frac{l n ( 0.5 )}{2} )}{ln ( 0.5 )}

9^{x} - 4 (3^{x}) + 3 = 0

e^{x} + 12 e^{- x} - 7 = 0

1 6^{2 x} = 8^{x - 1}

100 = \frac{300}{1 + e ^{4 - t}}

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

What is the answer to \sqrt[x]{x}=sqrt(0.5) ?
The answer to \sqrt[x]{x}=sqrt(0.5) is x=-(2\W_{0}(-(ln(0.5))/2))/(ln(0.5))
Solve for x: \sqrt[x]{x}=sqrt(0.5)
The solution is x=-(2\W_{0}(-(ln(0.5))/2))/(ln(0.5))