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Otras calculadoras
-
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- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación x+18=8
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
-
Expresiones idénticas
- -log(y- cuatro)=Const-log(x+ tres)
- menos logaritmo de (y menos 4) es igual a Const menos logaritmo de (x más 3)
- menos logaritmo de (y menos cuatro) es igual a Const menos logaritmo de (x más tres)
- -logy-4=Const-logx+3
-
Expresiones semejantes
- -log(y-4)=Const+log(x+3)
- -log(y-4)=Const-log(x-3)
- log(y-4)=Const-log(x+3)
- -log(y+4)=Const-log(x+3)
-
Expresiones con funciones
- Logaritmo log
- log^24x−log4x^3+2=0
- log(4^x-b,2)=0
- log(1/6)*(x-5)=x+1
- log_2(3)=log_x(x^(2)-1)
- log(sin(x))-3*cos(x)=0
- Logaritmo log
- log^24x−log4x^3+2=0
- log(4^x-b,2)=0
- log(1/6)*(x-5)=x+1
- log_2(3)=log_x(x^(2)-1)
- log(sin(x))-3*cos(x)=0
-log(y-4)=Const-log(x+3) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
-log(y - 4) = c - log(x + 3)
$$- \log{\left(y - 4 \right)} = c - \log{\left(x + 3 \right)}$$
Solución detallada
Tenemos la ecuación
$$- \log{\left(y - 4 \right)} = c - \log{\left(x + 3 \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\log{\left(x + 3 \right)} = c + \log{\left(y - 4 \right)}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x + 3 = e^{\frac{c + \log{\left(y - 4 \right)}}{1}}$$
simplificamos
$$x + 3 = \left(y - 4\right) e^{c}$$
$$x = \left(y - 4\right) e^{c} - 3$$
$$- \log{\left(y - 4 \right)} = c - \log{\left(x + 3 \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\log{\left(x + 3 \right)} = c + \log{\left(y - 4 \right)}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x + 3 = e^{\frac{c + \log{\left(y - 4 \right)}}{1}}$$
simplificamos
$$x + 3 = \left(y - 4\right) e^{c}$$
$$x = \left(y - 4\right) e^{c} - 3$$
Gráfica
Suma y producto de raíces
[src]
suma
/ re(c) re(c) \ re(c) re(c) -3 + I*\(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 3$$
=
/ re(c) re(c) \ re(c) re(c) -3 + I*\(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 3$$
producto
/ re(c) re(c) \ re(c) re(c) -3 + I*\(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 3$$
=
re(c) re(c) re(c) -3 + I*((-4 + re(y))*sin(im(c)) + cos(im(c))*im(y))*e + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} - 4\right) \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) e^{\operatorname{re}{\left(c\right)}} + \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 3$$
-3 + i*((-4 + re(y))*sin(im(c)) + cos(im(c))*im(y))*exp(re(c)) + (-4 + re(y))*cos(im(c))*exp(re(c)) - exp(re(c))*im(y)*sin(im(c))
Respuesta rápida
[src]
/ re(c) re(c) \ re(c) re(c) x1 = -3 + I*\(-4 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (-4 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$x_{1} = i \left(\left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} - 4\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 3$$
x1 = i*((re(y) - 4)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y)) + (re(y) - 4)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 3