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4lg2x+2lgx–2=0 equation

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Numerical solution:

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The solution

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4*log(2*x) + 2*log(x) - 2 = 0
$$\left(2 \log{\left(x \right)} + 4 \log{\left(2 x \right)}\right) - 2 = 0$$
The graph
Rapid solution [src]
     3 ___  1/3
     \/ 2 *e   
x1 = ----------
         2     
$$x_{1} = \frac{\sqrt[3]{2} e^{\frac{1}{3}}}{2}$$
x1 = 2^(1/3)*exp(1/3)/2
Sum and product of roots [src]
sum
3 ___  1/3
\/ 2 *e   
----------
    2     
$$\frac{\sqrt[3]{2} e^{\frac{1}{3}}}{2}$$
=
3 ___  1/3
\/ 2 *e   
----------
    2     
$$\frac{\sqrt[3]{2} e^{\frac{1}{3}}}{2}$$
product
3 ___  1/3
\/ 2 *e   
----------
    2     
$$\frac{\sqrt[3]{2} e^{\frac{1}{3}}}{2}$$
=
3 ___  1/3
\/ 2 *e   
----------
    2     
$$\frac{\sqrt[3]{2} e^{\frac{1}{3}}}{2}$$
2^(1/3)*exp(1/3)/2
Numerical answer [src]
x1 = 0.879180735930398
x1 = 0.879180735930398