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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x)^(3/(x+3))*log(x)^2*log(x/4)/x

¿Cómo vas a descomponer esta log(x)^(3/(x+3))*log(x)^2*log(x/4)/x expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
          3                 
        -----               
        x + 3    2       /x\
(log(x))     *log (x)*log|-|
                         \4/
----------------------------
             x
log⁡(x)2log⁡(x)3x+3log⁡(x4)x\frac{\log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}} \log{\left(\frac{x}{4} \right)}}{x} 
((log(x)^(3/(x + 3))*log(x)^2)*log(x/4))/x
Simplificación general [src] 
              3         
        2 + -----       
            3 + x    /x\
(log(x))         *log|-|
                     \4/
------------------------
           x
log⁡(x4)log⁡(x)2+3x+3x\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2 + \frac{3}{x + 3}}}{x} 
log(x)^(2 + 3/(3 + x))*log(x/4)/x
Respuesta numérica [src] 
log(x)^2*log(x)^(3.0/(3.0 + x))*log(x/4)/x
log(x)^2*log(x)^(3.0/(3.0 + x))*log(x/4)/x
Parte trigonométrica [src] 
                  3         
                -----       
   2            3 + x    /x\
log (x)*(log(x))     *log|-|
                         \4/
----------------------------
             x
log⁡(x4)log⁡(x)2log⁡(x)3x+3x\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x} 
log(x)^2*log(x)^(3/(3 + x))*log(x/4)/x
Denominador común [src] 
 /                    3                         3         \ 
 |                  -----                     -----       | 
 |     3            3 + x        2            3 + x       | 
-\- log (x)*(log(x))      + 2*log (x)*(log(x))     *log(2)/ 
------------------------------------------------------------
                             x
−−log⁡(x)3log⁡(x)3x+3+2log⁡(2)log⁡(x)2log⁡(x)3x+3x- \frac{- \log{\left(x \right)}^{3} \log{\left(x \right)}^{\frac{3}{x + 3}} + 2 \log{\left(2 \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x} 
-(-log(x)^3*log(x)^(3/(3 + x)) + 2*log(x)^2*log(x)^(3/(3 + x))*log(2))/x
Potencias [src] 
              3         
        2 + -----       
            3 + x    /x\
(log(x))         *log|-|
                     \4/
------------------------
           x
log⁡(x4)log⁡(x)2+3x+3x\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2 + \frac{3}{x + 3}}}{x} 
                  3         
                -----       
   2            3 + x    /x\
log (x)*(log(x))     *log|-|
                         \4/
----------------------------
             x
log⁡(x4)log⁡(x)2log⁡(x)3x+3x\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x} 
         1                 
       -----               
       3 + x               
   3            2       /x\
log (x)     *log (x)*log|-|
                        \4/
---------------------------
             x
(log⁡(x)3)1x+3log⁡(x4)log⁡(x)2x\frac{\left(\log{\left(x \right)}^{3}\right)^{\frac{1}{x + 3}} \log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2}}{x} 
(log(x)^3)^(1/(3 + x))*log(x)^2*log(x/4)/x
Combinatoria [src] 
                   3                        
                 -----                      
    2            3 + x                      
-log (x)*(log(x))     *(-log(x) + 2*log(2)) 
--------------------------------------------
                     x
−(−log⁡(x)+2log⁡(2))log⁡(x)2log⁡(x)3x+3x- \frac{\left(- \log{\left(x \right)} + 2 \log{\left(2 \right)}\right) \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x} 
-log(x)^2*log(x)^(3/(3 + x))*(-log(x) + 2*log(2))/x
Unión de expresiones racionales [src] 
                  3         
                -----       
   2            3 + x    /x\
log (x)*(log(x))     *log|-|
                         \4/
----------------------------
             x
log⁡(x4)log⁡(x)2log⁡(x)3x+3x\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x} 
log(x)^2*log(x)^(3/(3 + x))*log(x/4)/x
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