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1/(2-(log(2)/log(x)))+1/((log(2)/log(x)))=3/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
    1           1          
---------- + -------- = 3/2
    log(2)   /log(2)\      
2 - ------   |------|      
    log(x)   \log(x)/      
$$\frac{1}{2 - \frac{\log{\left(2 \right)}}{\log{\left(x \right)}}} + \frac{1}{\log{\left(2 \right)} \frac{1}{\log{\left(x \right)}}} = \frac{3}{2}$$
Gráfica
Respuesta rápida [src]
             /  ___       \             /  ___       \
      3/4    |\/ 3 *log(2)|      3/4    |\/ 3 *log(2)|
x1 = 2   *cos|------------| - I*2   *sin|------------|
             \     4      /             \     4      /
$$x_{1} = 2^{\frac{3}{4}} \cos{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)} - 2^{\frac{3}{4}} i \sin{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)}$$
             /  ___       \             /  ___       \
      3/4    |\/ 3 *log(2)|      3/4    |\/ 3 *log(2)|
x2 = 2   *cos|------------| + I*2   *sin|------------|
             \     4      /             \     4      /
$$x_{2} = 2^{\frac{3}{4}} \cos{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)} + 2^{\frac{3}{4}} i \sin{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)}$$
x2 = 2^(3/4)*cos(sqrt(3)*log(2)/4) + 2^(3/4)*i*sin(sqrt(3)*log(2)/4)
Suma y producto de raíces [src]
suma
        /  ___       \             /  ___       \           /  ___       \             /  ___       \
 3/4    |\/ 3 *log(2)|      3/4    |\/ 3 *log(2)|    3/4    |\/ 3 *log(2)|      3/4    |\/ 3 *log(2)|
2   *cos|------------| - I*2   *sin|------------| + 2   *cos|------------| + I*2   *sin|------------|
        \     4      /             \     4      /           \     4      /             \     4      /
$$\left(2^{\frac{3}{4}} \cos{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)} - 2^{\frac{3}{4}} i \sin{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)}\right) + \left(2^{\frac{3}{4}} \cos{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)} + 2^{\frac{3}{4}} i \sin{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)}\right)$$
=
          /  ___       \
   3/4    |\/ 3 *log(2)|
2*2   *cos|------------|
          \     4      /
$$2 \cdot 2^{\frac{3}{4}} \cos{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)}$$
producto
/        /  ___       \             /  ___       \\ /        /  ___       \             /  ___       \\
| 3/4    |\/ 3 *log(2)|      3/4    |\/ 3 *log(2)|| | 3/4    |\/ 3 *log(2)|      3/4    |\/ 3 *log(2)||
|2   *cos|------------| - I*2   *sin|------------||*|2   *cos|------------| + I*2   *sin|------------||
\        \     4      /             \     4      // \        \     4      /             \     4      //
$$\left(2^{\frac{3}{4}} \cos{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)} - 2^{\frac{3}{4}} i \sin{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)}\right) \left(2^{\frac{3}{4}} \cos{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)} + 2^{\frac{3}{4}} i \sin{\left(\frac{\sqrt{3} \log{\left(2 \right)}}{4} \right)}\right)$$
=
    ___
2*\/ 2 
$$2 \sqrt{2}$$
2*sqrt(2)
Respuesta numérica [src]
x1 = 1.60660769937748 - 0.497231158564308*i
x2 = 1.60660769937748 + 0.497231158564308*i
x2 = 1.60660769937748 + 0.497231158564308*i