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- La ecuación:
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Ecuación 3x-2(3x+4)=10
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Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
-
Ecuación 6*3+x=72
- Expresar {x} en función de y en la ecuación:
- 7*x-1*y=0
- -18*x-6*y=-1
- 13*x-12*y=19
- 6*x+9*y=-9
-
Expresiones idénticas
- log(dos *x+ uno)/ dos =e^c*(y+ uno)
- logaritmo de (2 multiplicar por x más 1) dividir por 2 es igual a e en el grado c multiplicar por (y más 1)
- logaritmo de (dos multiplicar por x más uno) dividir por dos es igual a e en el grado c multiplicar por (y más uno)
- log(2*x+1)/2=ec*(y+1)
- log2*x+1/2=ec*y+1
- log(2x+1)/2=e^c(y+1)
- log(2x+1)/2=ec(y+1)
- log2x+1/2=ecy+1
- log2x+1/2=e^cy+1
- log(2*x+1) dividir por 2=e^c*(y+1)
-
Expresiones semejantes
- log(2*x-1)/2=e^c*(y+1)
- log(2*x+1)/2=e^c*(y-1)
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Expresiones con funciones
- Logaritmo log
- log(x+1)=2*(x-2)^2
- log1÷2(x^2+4x-5)=-4
- log((2,2)+log(3,3+x))=0
- log(2/3)=(x*x-16)
- log(8)*x=2+x
log(2*x+1)/2=e^c*(y+1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(2*x + 1) c
------------ = E *(y + 1)
2
$$\frac{\log{\left(2 x + 1 \right)}}{2} = e^{c} \left(y + 1\right)$$
Solución detallada
Tenemos la ecuación
$$\frac{\log{\left(2 x + 1 \right)}}{2} = e^{c} \left(y + 1\right)$$
$$\frac{\log{\left(2 x + 1 \right)}}{2} = \left(y + 1\right) e^{c}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =1/2
$$\log{\left(2 x + 1 \right)} = 2 \left(y + 1\right) e^{c}$$
Es la ecuación de la forma:
Por definición log
entonces
simplificamos
$$2 x + 1 = e^{2 \left(y + 1\right) e^{c}}$$
$$2 x = e^{2 \left(y + 1\right) e^{c}} - 1$$
$$x = \frac{e^{2 \left(y + 1\right) e^{c}}}{2} - \frac{1}{2}$$
$$\frac{\log{\left(2 x + 1 \right)}}{2} = e^{c} \left(y + 1\right)$$
$$\frac{\log{\left(2 x + 1 \right)}}{2} = \left(y + 1\right) e^{c}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =1/2
$$\log{\left(2 x + 1 \right)} = 2 \left(y + 1\right) e^{c}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
c
(1 + y)*e
----------
1/2
2*x + 1 = e simplificamos
$$2 x + 1 = e^{2 \left(y + 1\right) e^{c}}$$
$$2 x = e^{2 \left(y + 1\right) e^{c}} - 1$$
$$x = \frac{e^{2 \left(y + 1\right) e^{c}}}{2} - \frac{1}{2}$$
Gráfica
Respuesta rápida
[src]
re(c) re(c) re(c) re(c) re(c) re(c)
/ re(c) re(c) re(c) \ 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) / re(c) re(c) re(c) \
1 cos\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/*e I*e *sin\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/
x1 = - - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2
$$x_{1} = \frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}$$
x1 = i*exp(-2*exp(re(c))*sin(im(c))*im(y) + 2*exp(re(c))*cos(im(c))*re(y) + 2*exp(re(c))*cos(im(c)))*sin(2*exp(re(c))*sin(im(c))*re(y) + 2*exp(re(c))*sin(im(c)) + 2*exp(re(c))*cos(im(c))*im(y))/2 + exp(-2*exp(re(c))*sin(im(c))*im(y) + 2*exp(re(c))*cos(im(c))*re(y) + 2*exp(re(c))*cos(im(c)))*cos(2*exp(re(c))*sin(im(c))*re(y) + 2*exp(re(c))*sin(im(c)) + 2*exp(re(c))*cos(im(c))*im(y))/2 - 1/2
Suma y producto de raíces
[src]
suma
re(c) re(c) re(c) re(c) re(c) re(c)
/ re(c) re(c) re(c) \ 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) / re(c) re(c) re(c) \
1 cos\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/*e I*e *sin\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/
- - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2
$$\frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}$$
=
re(c) re(c) re(c) re(c) re(c) re(c)
/ re(c) re(c) re(c) \ 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) / re(c) re(c) re(c) \
1 cos\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/*e I*e *sin\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/
- - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2
$$\frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}$$
producto
re(c) re(c) re(c) re(c) re(c) re(c)
/ re(c) re(c) re(c) \ 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) 2*cos(im(c))*e - 2*e *im(y)*sin(im(c)) + 2*cos(im(c))*e *re(y) / re(c) re(c) re(c) \
1 cos\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/*e I*e *sin\2*e *sin(im(c)) + 2*cos(im(c))*e *im(y) + 2*e *re(y)*sin(im(c))/
- - + ------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2
$$\frac{i e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \sin{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} + \frac{e^{- 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)}} \cos{\left(2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + 2 e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + 2 e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} \right)}}{2} - \frac{1}{2}$$
=
re(c) re(c)
/ re(c)\ 2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*e 2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*e / re(c)\
1 cos\2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*e /*e I*e *sin\2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*e /
- - + ----------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------
2 2 2
$$\frac{i e^{2 \left(- \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)}\right) e^{\operatorname{re}{\left(c\right)}}} \sin{\left(2 \left(\sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) e^{\operatorname{re}{\left(c\right)}} \right)}}{2} + \frac{e^{2 \left(- \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)}\right) e^{\operatorname{re}{\left(c\right)}}} \cos{\left(2 \left(\sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{re}{\left(y\right)} + \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) e^{\operatorname{re}{\left(c\right)}} \right)}}{2} - \frac{1}{2}$$
-1/2 + cos(2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*exp(re(c)))*exp(2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*exp(re(c)))/2 + i*exp(2*(cos(im(c))*re(y) - im(y)*sin(im(c)) + cos(im(c)))*exp(re(c)))*sin(2*(cos(im(c))*im(y) + re(y)*sin(im(c)) + sin(im(c)))*exp(re(c)))/2