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- La ecuación:
-
Ecuación 6*x^2+x-7=0
-
Ecuación 2-5(3+2x)=17
-
Ecuación (6*x+8)/2+5=5*x/3
-
Ecuación 2,6x-0,75=0,9x-35,6
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- -10*x-12*y=-10
-
Expresiones idénticas
- -log(y+ uno)=Const-log(x+ uno)
- menos logaritmo de (y más 1) es igual a Const menos logaritmo de (x más 1)
- menos logaritmo de (y más uno) es igual a Const menos logaritmo de (x más uno)
- -logy+1=Const-logx+1
-
Expresiones semejantes
- -log(y+1)=Const+log(x+1)
- -log(y-1)=Const-log(x+1)
- -log(y+1)=Const-log(x-1)
- log(y+1)=Const-log(x+1)
-
Expresiones con funciones
- Logaritmo log
- log(b)-log(a)=y
- log3^2x=4-3log3x
- log1/4(x+5)=1/2
- log(x+5)-x^2=0
- log2(x+3)=1
- Logaritmo log
- log(b)-log(a)=y
- log3^2x=4-3log3x
- log1/4(x+5)=1/2
- log(x+5)-x^2=0
- log2(x+3)=1
-log(y+1)=Const-log(x+1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
-log(y + 1) = c - log(x + 1)
$$- \log{\left(y + 1 \right)} = c - \log{\left(x + 1 \right)}$$
Solución detallada
Tenemos la ecuación
$$- \log{\left(y + 1 \right)} = c - \log{\left(x + 1 \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\log{\left(x + 1 \right)} = c + \log{\left(y + 1 \right)}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x + 1 = e^{\frac{c + \log{\left(y + 1 \right)}}{1}}$$
simplificamos
$$x + 1 = \left(y + 1\right) e^{c}$$
$$x = \left(y + 1\right) e^{c} - 1$$
$$- \log{\left(y + 1 \right)} = c - \log{\left(x + 1 \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\log{\left(x + 1 \right)} = c + \log{\left(y + 1 \right)}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x + 1 = e^{\frac{c + \log{\left(y + 1 \right)}}{1}}$$
simplificamos
$$x + 1 = \left(y + 1\right) e^{c}$$
$$x = \left(y + 1\right) e^{c} - 1$$
Gráfica
Respuesta rápida
[src]
/ re(c) re(c) \ re(c) re(c) x1 = -1 + I*\(1 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (1 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$x_{1} = i \left(\left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1$$
x1 = i*((re(y) + 1)*exp(re(c))*sin(im(c)) + exp(re(c))*cos(im(c))*im(y)) + (re(y) + 1)*exp(re(c))*cos(im(c)) - exp(re(c))*sin(im(c))*im(y) - 1
Suma y producto de raíces
[src]
suma
/ re(c) re(c) \ re(c) re(c) -1 + I*\(1 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (1 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1$$
=
/ re(c) re(c) \ re(c) re(c) -1 + I*\(1 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (1 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1$$
producto
/ re(c) re(c) \ re(c) re(c) -1 + I*\(1 + re(y))*e *sin(im(c)) + cos(im(c))*e *im(y)/ + (1 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} + e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1$$
=
re(c) re(c) re(c) -1 + I*((1 + re(y))*sin(im(c)) + cos(im(c))*im(y))*e + (1 + re(y))*cos(im(c))*e - e *im(y)*sin(im(c))
$$i \left(\left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\operatorname{im}{\left(c\right)} \right)} + \cos{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)}\right) e^{\operatorname{re}{\left(c\right)}} + \left(\operatorname{re}{\left(y\right)} + 1\right) e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} \operatorname{im}{\left(y\right)} - 1$$
-1 + i*((1 + re(y))*sin(im(c)) + cos(im(c))*im(y))*exp(re(c)) + (1 + re(y))*cos(im(c))*exp(re(c)) - exp(re(c))*im(y)*sin(im(c))