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Otras calculadoras
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¿Cómo usar?
- La ecuación:
-
Ecuación 12/(x+3)=-6/7
-
Ecuación (x-6)(4x-6)=0
-
Ecuación (x+7)^3=9*(x+7)
-
Ecuación z^2+z+1=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 7*x-1*y=0
- -9*x-1*y=6
- -2*x+2*y=4
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Expresiones idénticas
- log(y+ uno)=Const-log(x- uno)
- logaritmo de (y más 1) es igual a Const menos logaritmo de (x menos 1)
- logaritmo de (y más uno) es igual a Const menos logaritmo de (x menos uno)
- logy+1=Const-logx-1
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Expresiones semejantes
- (-log(log(y)+1))/3=c-x^1
- log(y+1)=Const+log(x-1)
- log(y+1)=Const-log(x+1)
- (log(y)+1)/y=c-log(x)
- log(y)+1/y=1/x+log(x)
- log(y-1)=Const-log(x-1)
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Expresiones con funciones
- Logaritmo log
- log(3)*27=x
- log(1)/9=2+x
- log(4/(7-x))/log(x^2)=11
- log(4*3^(x-1)-1)/log(3)=2*x-1
- log3(2x^2+x)=log3(6)-log3(2)
- Logaritmo log
- log(3)*27=x
- log(1)/9=2+x
- log(4/(7-x))/log(x^2)=11
- log(4*3^(x-1)-1)/log(3)=2*x-1
- log3(2x^2+x)=log3(6)-log3(2)
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
$$\log{\left(y + 1 \right)} = c - \log{\left(x - 1 \right)}$$
$$\log{\left(y + 1 \right)} = c - \log{\left(x - 1 \right)}$$
Es la ecuación de la forma:
Por definición log
entonces
$$y + 1 = e^{\frac{c - \log{\left(x - 1 \right)}}{1}}$$
simplificamos
$$y + 1 = \frac{e^{c}}{x - 1}$$
$$y = -1 + \frac{e^{c}}{x - 1}$$
$$\log{\left(y + 1 \right)} = c - \log{\left(x - 1 \right)}$$
$$\log{\left(y + 1 \right)} = c - \log{\left(x - 1 \right)}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$y + 1 = e^{\frac{c - \log{\left(x - 1 \right)}}{1}}$$
simplificamos
$$y + 1 = \frac{e^{c}}{x - 1}$$
$$y = -1 + \frac{e^{c}}{x - 1}$$
Gráfica
Suma y producto de raíces
[src]
suma
/ / re(c) \ / re(c)\ \ / re(c)\ / re(c) \ |(-1 + re(x))*\-im(x) + e *sin(im(c))/ \1 - re(x) + cos(im(c))*e /*im(x)| (-1 + re(x))*\1 - re(x) + cos(im(c))*e / \-im(x) + e *sin(im(c))/*im(x) I*|----------------------------------------- - -------------------------------------| + -------------------------------------------- + ---------------------------------- | 2 2 2 2 | 2 2 2 2 \ (-1 + re(x)) + im (x) (-1 + re(x)) + im (x) / (-1 + re(x)) + im (x) (-1 + re(x)) + im (x)
$$\frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
=
/ / re(c) \ / re(c)\ \ / re(c)\ / re(c) \ |(-1 + re(x))*\-im(x) + e *sin(im(c))/ \1 - re(x) + cos(im(c))*e /*im(x)| (-1 + re(x))*\1 - re(x) + cos(im(c))*e / \-im(x) + e *sin(im(c))/*im(x) I*|----------------------------------------- - -------------------------------------| + -------------------------------------------- + ---------------------------------- | 2 2 2 2 | 2 2 2 2 \ (-1 + re(x)) + im (x) (-1 + re(x)) + im (x) / (-1 + re(x)) + im (x) (-1 + re(x)) + im (x)
$$\frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
producto
/ / re(c) \ / re(c)\ \ / re(c)\ / re(c) \ |(-1 + re(x))*\-im(x) + e *sin(im(c))/ \1 - re(x) + cos(im(c))*e /*im(x)| (-1 + re(x))*\1 - re(x) + cos(im(c))*e / \-im(x) + e *sin(im(c))/*im(x) I*|----------------------------------------- - -------------------------------------| + -------------------------------------------- + ---------------------------------- | 2 2 2 2 | 2 2 2 2 \ (-1 + re(x)) + im (x) (-1 + re(x)) + im (x) / (-1 + re(x)) + im (x) (-1 + re(x)) + im (x)
$$\frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
=
/ / re(c) \ / re(c)\ \ / re(c)\ / re(c) \
I*\(-1 + re(x))*\-im(x) + e *sin(im(c))/ - \1 - re(x) + cos(im(c))*e /*im(x)/ + (-1 + re(x))*\1 - re(x) + cos(im(c))*e / + \-im(x) + e *sin(im(c))/*im(x)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
(-1 + re(x)) + im (x)
$$\frac{i \left(\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 1\right) - \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}\right) + \left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)} + \left(\operatorname{re}{\left(x\right)} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
(i*((-1 + re(x))*(-im(x) + exp(re(c))*sin(im(c))) - (1 - re(x) + cos(im(c))*exp(re(c)))*im(x)) + (-1 + re(x))*(1 - re(x) + cos(im(c))*exp(re(c))) + (-im(x) + exp(re(c))*sin(im(c)))*im(x))/((-1 + re(x))^2 + im(x)^2)
Respuesta rápida
[src]
/ / re(c) \ / re(c)\ \ / re(c)\ / re(c) \
|(-1 + re(x))*\-im(x) + e *sin(im(c))/ \1 - re(x) + cos(im(c))*e /*im(x)| (-1 + re(x))*\1 - re(x) + cos(im(c))*e / \-im(x) + e *sin(im(c))/*im(x)
y1 = I*|----------------------------------------- - -------------------------------------| + -------------------------------------------- + ----------------------------------
| 2 2 2 2 | 2 2 2 2
\ (-1 + re(x)) + im (x) (-1 + re(x)) + im (x) / (-1 + re(x)) + im (x) (-1 + re(x)) + im (x)
$$y_{1} = \frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + i \left(\frac{\left(e^{\operatorname{re}{\left(c\right)}} \sin{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{im}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(e^{\operatorname{re}{\left(c\right)}} \cos{\left(\operatorname{im}{\left(c\right)} \right)} - \operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
y1 = (exp(re(c))*sin(im(c)) - im(x))*im(x)/((re(x) - 1)^2 + im(x)^2) + i*((exp(re(c))*sin(im(c)) - im(x))*(re(x) - 1)/((re(x) - 1)^2 + im(x)^2) - (exp(re(c))*cos(im(c)) - re(x) + 1)*im(x)/((re(x) - 1)^2 + im(x)^2)) + (re(x) - 1)*(exp(re(c))*cos(im(c)) - re(x) + 1)/((re(x) - 1)^2 + im(x)^2)