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log^3x+4log^3x=9 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   3           3       
log (x) + 4*log (x) = 9
log⁡(x)3+4log⁡(x)3=9\log{\left(x \right)}^{3} + 4 \log{\left(x \right)}^{3} = 9
Simplificar
Gráfica
-7.5-5.0-2.50.02.55.07.510.012.515.017.520.0-20002000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
   2/3                         2/3          2/3                                            2/3          2/3                   
 15                         -15          -15                                            -15          -15                      
 -----      /  6 ___  2/3\  -------      -------    /  6 ___  2/3\      /  6 ___  2/3\  -------      -------    /  6 ___  2/3\
   5        |3*\/ 3 *5   |     10           10      |3*\/ 3 *5   |      |3*\/ 3 *5   |     10           10      |3*\/ 3 *5   |
e      + cos|------------|*e        - I*e       *sin|------------| + cos|------------|*e        + I*e       *sin|------------|
            \     10     /                          \     10     /      \     10     /                          \     10     /
(e15235+(cos⁡(336⋅52310)e152310−isin⁡(336⋅52310)e152310))+(cos⁡(336⋅52310)e152310+isin⁡(336⋅52310)e152310)\left(e^{\frac{15^{\frac{2}{3}}}{5}} + \left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} - \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right)\right) + \left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right) 
=
                        2/3       2/3
                     -15        15   
     /  6 ___  2/3\  -------    -----
     |3*\/ 3 *5   |     10        5  
2*cos|------------|*e        + e     
     \     10     /
2cos⁡(336⋅52310)e152310+e15235\frac{2 \cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + e^{\frac{15^{\frac{2}{3}}}{5}} 
producto
   2/3 /                      2/3          2/3                   \ /                      2/3          2/3                   \
 15    |                   -15          -15                      | |                   -15          -15                      |
 ----- |   /  6 ___  2/3\  -------      -------    /  6 ___  2/3\| |   /  6 ___  2/3\  -------      -------    /  6 ___  2/3\|
   5   |   |3*\/ 3 *5   |     10           10      |3*\/ 3 *5   || |   |3*\/ 3 *5   |     10           10      |3*\/ 3 *5   ||
e     *|cos|------------|*e        - I*e       *sin|------------||*|cos|------------|*e        + I*e       *sin|------------||
       \   \     10     /                          \     10     // \   \     10     /                          \     10     //
(cos⁡(336⋅52310)e152310−isin⁡(336⋅52310)e152310)e15235(cos⁡(336⋅52310)e152310+isin⁡(336⋅52310)e152310)\left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} - \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right) e^{\frac{15^{\frac{2}{3}}}{5}} \left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right) 
=
1
11 
1
Respuesta rápida [src] 
        2/3
      15   
      -----
        5  
x1 = e
x1=e15235x_{1} = e^{\frac{15^{\frac{2}{3}}}{5}} 
                           2/3          2/3                   
                        -15          -15                      
        /  6 ___  2/3\  -------      -------    /  6 ___  2/3\
        |3*\/ 3 *5   |     10           10      |3*\/ 3 *5   |
x2 = cos|------------|*e        - I*e       *sin|------------|
        \     10     /                          \     10     /
x2=cos⁡(336⋅52310)e152310−isin⁡(336⋅52310)e152310x_{2} = \frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} - \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} 
                           2/3          2/3                   
                        -15          -15                      
        /  6 ___  2/3\  -------      -------    /  6 ___  2/3\
        |3*\/ 3 *5   |     10           10      |3*\/ 3 *5   |
x3 = cos|------------|*e        + I*e       *sin|------------|
        \     10     /                          \     10     /
x3=cos⁡(336⋅52310)e152310+isin⁡(336⋅52310)e152310x_{3} = \frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} 
x3 = exp(-15^(2/3)/10)*cos(3*3^(1/6)*5^(2/3)/10) + i*exp(-15^(2/3)/10)*sin(3*3^(1/6)*5^(2/3)/10)
Respuesta numérica [src] 
x1 = 3.37515213084549
x2 = 0.269198074615172 - 0.473091257293331*i
x3 = 0.269198074615172 + 0.473091257293331*i
x3 = 0.269198074615172 + 0.473091257293331*i
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