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lg^2(x)-lg^2(10x)=6-lg^2(100x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   2         2                2       
log (x) - log (10*x) = 6 - log (100*x)
log⁡(x)2−log⁡(10x)2=6−log⁡(100x)2\log{\left(x \right)}^{2} - \log{\left(10 x \right)}^{2} = 6 - \log{\left(100 x \right)}^{2}
Simplificar
Gráfica
0.01.02.03.04.05.06.07.08.09.010.0-5050
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
        /         _______________\        /         _______________\
        |  ___   /         2     |        |  ___   /         2     |
     cos\\/ 2 *\/  -3 + log (10) /   I*sin\\/ 2 *\/  -3 + log (10) /
x1 = ----------------------------- - -------------------------------
                   10                               10
x1=cos⁡(2−3+log⁡(10)2)10−isin⁡(2−3+log⁡(10)2)10x_{1} = \frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} - \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} 
        /         _______________\        /         _______________\
        |  ___   /         2     |        |  ___   /         2     |
     cos\\/ 2 *\/  -3 + log (10) /   I*sin\\/ 2 *\/  -3 + log (10) /
x2 = ----------------------------- + -------------------------------
                   10                               10
x2=cos⁡(2−3+log⁡(10)2)10+isin⁡(2−3+log⁡(10)2)10x_{2} = \frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} + \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} 
x2 = cos(sqrt(2)*sqrt(-3 + log(10)^2))/10 + i*sin(sqrt(2)*sqrt(-3 + log(10)^2))/10
Suma y producto de raíces [src] 
suma
   /         _______________\        /         _______________\      /         _______________\        /         _______________\
   |  ___   /         2     |        |  ___   /         2     |      |  ___   /         2     |        |  ___   /         2     |
cos\\/ 2 *\/  -3 + log (10) /   I*sin\\/ 2 *\/  -3 + log (10) /   cos\\/ 2 *\/  -3 + log (10) /   I*sin\\/ 2 *\/  -3 + log (10) /
----------------------------- - ------------------------------- + ----------------------------- + -------------------------------
              10                               10                               10                               10
(cos⁡(2−3+log⁡(10)2)10−isin⁡(2−3+log⁡(10)2)10)+(cos⁡(2−3+log⁡(10)2)10+isin⁡(2−3+log⁡(10)2)10)\left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} - \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right) + \left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} + \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right) 
=
   /         _______________\
   |  ___   /         2     |
cos\\/ 2 *\/  -3 + log (10) /
-----------------------------
              5
cos⁡(2−3+log⁡(10)2)5\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{5} 
producto
/   /         _______________\        /         _______________\\ /   /         _______________\        /         _______________\\
|   |  ___   /         2     |        |  ___   /         2     || |   |  ___   /         2     |        |  ___   /         2     ||
|cos\\/ 2 *\/  -3 + log (10) /   I*sin\\/ 2 *\/  -3 + log (10) /| |cos\\/ 2 *\/  -3 + log (10) /   I*sin\\/ 2 *\/  -3 + log (10) /|
|----------------------------- - -------------------------------|*|----------------------------- + -------------------------------|
\              10                               10              / \              10                               10              /
(cos⁡(2−3+log⁡(10)2)10−isin⁡(2−3+log⁡(10)2)10)(cos⁡(2−3+log⁡(10)2)10+isin⁡(2−3+log⁡(10)2)10)\left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} - \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right) \left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} + \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right) 
=
1/100
1100\frac{1}{100} 
1/100
Respuesta numérica [src] 
x1 = -0.0543708526551129 - 0.0839274113836237*i
x2 = -0.0543708526551129 + 0.0839274113836237*i
x2 = -0.0543708526551129 + 0.0839274113836237*i
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