Sr Examen

Otras calculadoras

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

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
    1           1          
---------- + -------- = 3/2
    log(2)   /log(2)\      
2 - ------   |------|      
    log(x)   \log(x)/
12−log⁡(2)log⁡(x)+1log⁡(2)1log⁡(x)=32\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}
Simplificar
Gráfica
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.515.010.012.5-20002000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
             /  ___       \             /  ___       \
      3/4    |\/ 3 *log(2)|      3/4    |\/ 3 *log(2)|
x1 = 2   *cos|------------| - I*2   *sin|------------|
             \     4      /             \     4      /
x1=234cos⁡(3log⁡(2)4)−234isin⁡(3log⁡(2)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      /
x2=234cos⁡(3log⁡(2)4)+234isin⁡(3log⁡(2)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      /
(234cos⁡(3log⁡(2)4)−234isin⁡(3log⁡(2)4))+(234cos⁡(3log⁡(2)4)+234isin⁡(3log⁡(2)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⋅234cos⁡(3log⁡(2)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      //
(234cos⁡(3log⁡(2)4)−234isin⁡(3log⁡(2)4))(234cos⁡(3log⁡(2)4)+234isin⁡(3log⁡(2)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
222 \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
    © Sr Examen – Калькулятор