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Otras calculadoras
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- La ecuación:
-
Ecuación x+9=0
-
Ecuación 2x^2+7x-9=0
-
Ecuación 5*x^2+9*x=0
-
Ecuación 3x^2=2x+x^3
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -14*x+4*y=-16
- 11*x-9*y=-4
- Derivada de:
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log(y)
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x^5/5
- Integral de d{x}:
- log(y)
- Gráfico de la función y =:
- log(y)
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x^5/5
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Expresiones idénticas
- log(y)=x^ cinco / cinco
- logaritmo de (y) es igual a x en el grado 5 dividir por 5
- logaritmo de (y) es igual a x en el grado cinco dividir por cinco
- log(y)=x5/5
- logy=x5/5
- log(y)=x⁵/5
- logy=x^5/5
- log(y)=x^5 dividir por 5
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Expresiones semejantes
- log(y/x)=c*x
-
Expresiones con funciones
- Logaritmo log
- log(9-16x^4,3-4x^2)=2+(1/(log(3-4x^2,2)))
- log(2)*(log(3)*(log(4)*(1x-1)))=1
- log1-x(a-x+2)=2
- log(10,x)^2+log(10,x^2)=log(10,2)-1
- log(1/3)^x=3
log(y)=x^5/5 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\log{\left(y \right)} = \frac{x^{5}}{5}$$
$$\log{\left(y \right)} = \frac{x^{5}}{5}$$
Es la ecuación de la forma:
Por definición log
entonces
$$y = e^{\frac{\frac{1}{5} x^{5}}{1}}$$
simplificamos
$$y = e^{\frac{x^{5}}{5}}$$
$$\log{\left(y \right)} = \frac{x^{5}}{5}$$
$$\log{\left(y \right)} = \frac{x^{5}}{5}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$y = e^{\frac{\frac{1}{5} x^{5}}{1}}$$
simplificamos
$$y = e^{\frac{x^{5}}{5}}$$
Gráfica
Respuesta rápida
[src]
5 5
re (x) 4 2 3 re (x) 4 2 3
/ 5 \ ------ + im (x)*re(x) - 2*im (x)*re (x) ------ + im (x)*re(x) - 2*im (x)*re (x) / 5 \
|im (x) 4 3 2 | 5 5 |im (x) 4 3 2 |
y1 = cos|------ + re (x)*im(x) - 2*im (x)*re (x)|*e + I*e *sin|------ + re (x)*im(x) - 2*im (x)*re (x)|
\ 5 / \ 5 /
$$y_{1} = i e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)} + e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)}$$
y1 = i*exp(re(x)^5/5 - 2*re(x)^3*im(x)^2 + re(x)*im(x)^4)*sin(re(x)^4*im(x) - 2*re(x)^2*im(x)^3 + im(x)^5/5) + exp(re(x)^5/5 - 2*re(x)^3*im(x)^2 + re(x)*im(x)^4)*cos(re(x)^4*im(x) - 2*re(x)^2*im(x)^3 + im(x)^5/5)
Suma y producto de raíces
[src]
suma
5 5
re (x) 4 2 3 re (x) 4 2 3
/ 5 \ ------ + im (x)*re(x) - 2*im (x)*re (x) ------ + im (x)*re(x) - 2*im (x)*re (x) / 5 \
|im (x) 4 3 2 | 5 5 |im (x) 4 3 2 |
cos|------ + re (x)*im(x) - 2*im (x)*re (x)|*e + I*e *sin|------ + re (x)*im(x) - 2*im (x)*re (x)|
\ 5 / \ 5 /
$$i e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)} + e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)}$$
=
5 5
re (x) 4 2 3 re (x) 4 2 3
/ 5 \ ------ + im (x)*re(x) - 2*im (x)*re (x) ------ + im (x)*re(x) - 2*im (x)*re (x) / 5 \
|im (x) 4 3 2 | 5 5 |im (x) 4 3 2 |
cos|------ + re (x)*im(x) - 2*im (x)*re (x)|*e + I*e *sin|------ + re (x)*im(x) - 2*im (x)*re (x)|
\ 5 / \ 5 /
$$i e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)} + e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)}$$
producto
5 5
re (x) 4 2 3 re (x) 4 2 3
/ 5 \ ------ + im (x)*re(x) - 2*im (x)*re (x) ------ + im (x)*re(x) - 2*im (x)*re (x) / 5 \
|im (x) 4 3 2 | 5 5 |im (x) 4 3 2 |
cos|------ + re (x)*im(x) - 2*im (x)*re (x)|*e + I*e *sin|------ + re (x)*im(x) - 2*im (x)*re (x)|
\ 5 / \ 5 /
$$i e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \sin{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)} + e^{\frac{\left(\operatorname{re}{\left(x\right)}\right)^{5}}{5} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{3} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{4}} \cos{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5} \right)}$$
=
/ 5 \ / 4 4 2 2 \ |im (x) 4 3 2 | \re (x) + 5*im (x) - 10*im (x)*re (x)/*re(x) I*|------ + re (x)*im(x) - 2*im (x)*re (x)| + -------------------------------------------- \ 5 / 5 e
$$e^{i \left(\left(\operatorname{re}{\left(x\right)}\right)^{4} \operatorname{im}{\left(x\right)} - 2 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{5}}{5}\right) + \frac{\left(\left(\operatorname{re}{\left(x\right)}\right)^{4} - 10 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 5 \left(\operatorname{im}{\left(x\right)}\right)^{4}\right) \operatorname{re}{\left(x\right)}}{5}}$$
exp(i*(im(x)^5/5 + re(x)^4*im(x) - 2*im(x)^3*re(x)^2) + (re(x)^4 + 5*im(x)^4 - 10*im(x)^2*re(x)^2)*re(x)/5)