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- La ecuación:
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Ecuación x^2-4x+5=0
-
Ecuación x^2+3x+2=0
-
Ecuación x^2+3x=4
-
Ecuación -x^2+5*x-6=0
- Expresar {x} en función de y en la ecuación:
- 10*x-2*y=0
- 1*x+4*y=20
- 3*x-7*y=13
- 13*x-15*y=-6
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Expresiones idénticas
- -y^ uno -y-log(y- uno)=(c+ uno)/x
- menos y en el grado 1 menos y menos logaritmo de (y menos 1) es igual a (c más 1) dividir por x
- menos y en el grado uno menos y menos logaritmo de (y menos uno) es igual a (c más uno) dividir por x
- -y1-y-log(y-1)=(c+1)/x
- -y1-y-logy-1=c+1/x
- -y^1-y-logy-1=c+1/x
- -y^1-y-log(y-1)=(c+1) dividir por x
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Expresiones semejantes
- -y^1-y+log(y-1)=(c+1)/x
- -y^1-y-log(y-1)=(c-1)/x
- y^1-y-log(y-1)=(c+1)/x
- -y^1-y-log(y+1)=(c+1)/x
- -y^1+y-log(y-1)=(c+1)/x
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Expresiones con funciones
- Logaritmo log
- log3x=-1
- log(4-4x)/log(2)=log(81)/log(2)
- log((3x-1),3)=1
- log(5)(x-2)sqrt(-x^2+4x+5)=0
- log3(-x)=2
-y^1-y-log(y-1)=(c+1)/x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
1 c + 1
- y - y - log(y - 1) = -----
x
$$\left(- y^{1} - y\right) - \log{\left(y - 1 \right)} = \frac{c + 1}{x}$$
Solución detallada
Tenemos la ecuación:
$$\left(- y^{1} - y\right) - \log{\left(y - 1 \right)} = \frac{c + 1}{x}$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
signo obtendremos la ecuación
$$\frac{x}{c + 1} = \frac{1}{- 2 y - \log{\left(y - 1 \right)}}$$
$$\frac{x}{c + 1} = \frac{1}{- 2 y - \log{\left(y - 1 \right)}}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Abrimos los paréntesis en el miembro derecho de la ecuación
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Dividamos ambos miembros de la ecuación en 1/(1 + c)
Obtenemos la respuesta: x = -(1 + c)/(2*y + log(-1 + y))
$$\left(- y^{1} - y\right) - \log{\left(y - 1 \right)} = \frac{c + 1}{x}$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
a1 = 1
b1 = 1/(-log(-1 + y) - 2*y)
a2 = 1
b2 = x/(1 + c)
signo obtendremos la ecuación
$$\frac{x}{c + 1} = \frac{1}{- 2 y - \log{\left(y - 1 \right)}}$$
$$\frac{x}{c + 1} = \frac{1}{- 2 y - \log{\left(y - 1 \right)}}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
x/1+/c = 1/(-log(-1 + y) - 2*y)
Abrimos los paréntesis en el miembro derecho de la ecuación
x/1+/c = -1/log-1/1+1/y - 2*y)
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
x/(1 + c) = -1/log-1/1+1/y - 2*y)
Dividamos ambos miembros de la ecuación en 1/(1 + c)
x = 1/(-log(-1 + y) - 2*y) / (1/(1 + c))
Obtenemos la respuesta: x = -(1 + c)/(2*y + log(-1 + y))
Gráfica
Respuesta rápida
[src]
/ (1 + re(c))*(-arg(-1 + y) - 2*im(y)) (2*re(y) + log(|-1 + y|))*im(c) \ (-arg(-1 + y) - 2*im(y))*im(c) (1 + re(c))*(2*re(y) + log(|-1 + y|))
x1 = I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - -----------------------------------------------------
| 2 2 2 2| 2 2 2 2
\ (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) / (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|))
$$x_{1} = i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}$$
x1 = i*(-(log(|y - 1|) + 2*re(y))*im(c)/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2) - (re(c) + 1)*(-2*im(y) - arg(y - 1))/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2)) - (log(|y - 1|) + 2*re(y))*(re(c) + 1)/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2) + (-2*im(y) - arg(y - 1))*im(c)/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2)
Suma y producto de raíces
[src]
suma
/ (1 + re(c))*(-arg(-1 + y) - 2*im(y)) (2*re(y) + log(|-1 + y|))*im(c) \ (-arg(-1 + y) - 2*im(y))*im(c) (1 + re(c))*(2*re(y) + log(|-1 + y|)) I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - ----------------------------------------------------- | 2 2 2 2| 2 2 2 2 \ (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) / (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|))
$$i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}$$
=
/ (1 + re(c))*(-arg(-1 + y) - 2*im(y)) (2*re(y) + log(|-1 + y|))*im(c) \ (-arg(-1 + y) - 2*im(y))*im(c) (1 + re(c))*(2*re(y) + log(|-1 + y|)) I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - ----------------------------------------------------- | 2 2 2 2| 2 2 2 2 \ (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) / (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|))
$$i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}$$
producto
/ (1 + re(c))*(-arg(-1 + y) - 2*im(y)) (2*re(y) + log(|-1 + y|))*im(c) \ (-arg(-1 + y) - 2*im(y))*im(c) (1 + re(c))*(2*re(y) + log(|-1 + y|)) I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - ----------------------------------------------------- | 2 2 2 2| 2 2 2 2 \ (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) / (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|)) (2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|))
$$i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}$$
=
I*((1 + re(c))*(2*im(y) + arg(-1 + y)) - (2*re(y) + log(|-1 + y|))*im(c)) - (1 + re(c))*(2*re(y) + log(|-1 + y|)) - (2*im(y) + arg(-1 + y))*im(c)
-------------------------------------------------------------------------------------------------------------------------------------------------
2 2
(2*im(y) + arg(-1 + y)) + (2*re(y) + log(|-1 + y|))
$$\frac{i \left(- \left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)} + \left(\operatorname{re}{\left(c\right)} + 1\right) \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)\right) - \left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right) - \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}$$
(i*((1 + re(c))*(2*im(y) + arg(-1 + y)) - (2*re(y) + log(|-1 + y|))*im(c)) - (1 + re(c))*(2*re(y) + log(|-1 + y|)) - (2*im(y) + arg(-1 + y))*im(c))/((2*im(y) + arg(-1 + y))^2 + (2*re(y) + log(|-1 + y|))^2)