What is the answer to log_{1/2}(x)=x ?

The answer to log_{1/2}(x)=x is x=(\W_{0}(ln(2)))/(ln(2))

Solve for x: log_{1/2}(x)=x

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

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lo g_{\frac{1}{2}} (x) = x

x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

Decimal Notation

x = 0.64118 \dots

Solution steps

lo g_{\frac{1}{2}} (x) = x

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

(\frac{1}{2})^{l o g_{\frac{1}{2}} (x)} = (\frac{1}{2})^{x}

Simplify

(\frac{1}{2})^{l o g_{\frac{1}{2}} (x)} : x

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

Solve

x = (\frac{1}{2})^{x} : x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

Verify Solutions:

x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

True

The solution is

x = \frac{W _{0} ( ln ( 2 ) )}{ln ( 2 )}

ln (3 x^{2} + 2 x) = 0

lo g_{3} (7 x - 1) = 3

lo g_{5} (9 x) + 2 lo g_{5} (3) = 2

12 lo g_{x} (5) + lo g_{5} (x) - 7 = 0

4 ln (x + 1) = 12

What is the answer to log_{1/2}(x)=x ?
The answer to log_{1/2}(x)=x is x=(\W_{0}(ln(2)))/(ln(2))
Solve for x: log_{1/2}(x)=x
The solution is x=(\W_{0}(ln(2)))/(ln(2))