Sr Examen
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?
Solución
Ha introducido
[src]
3
-----
x + 3 2 /x\
(log(x)) *log (x)*log|-|
\4/
----------------------------
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
$$\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2 + \frac{3}{x + 3}}}{x}$$
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
$$\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x}$$
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
$$- \frac{- \log{\left(x \right)}^{3} \log{\left(x \right)}^{\frac{3}{x + 3}} + 2 \log{\left(2 \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x}$$
-(-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
$$\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2 + \frac{3}{x + 3}}}{x}$$
3
-----
2 3 + x /x\
log (x)*(log(x)) *log|-|
\4/
----------------------------
x
$$\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x}$$
1
-----
3 + x
3 2 /x\
log (x) *log (x)*log|-|
\4/
---------------------------
x
$$\frac{\left(\log{\left(x \right)}^{3}\right)^{\frac{1}{x + 3}} \log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2}}{x}$$
(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
$$- \frac{\left(- \log{\left(x \right)} + 2 \log{\left(2 \right)}\right) \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x}$$
-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
$$\frac{\log{\left(\frac{x}{4} \right)} \log{\left(x \right)}^{2} \log{\left(x \right)}^{\frac{3}{x + 3}}}{x}$$
log(x)^2*log(x)^(3/(3 + x))*log(x/4)/x