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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 9-7(x+3)=5-6x
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Ecuación 4x-5=3+2(x+1)
-
Ecuación 6/(x-2)+5/x=3
- Expresar {x} en función de y en la ecuación:
- -14*x-12*y=-13
- -20*x+14*y=16
- -7*x+15*y=-11
- -14*x+5*y=3
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Expresiones idénticas
- (-log(u- uno)- cuatro)/(u- uno)=c+log(x- uno)
- ( menos logaritmo de (u menos 1) menos 4) dividir por (u menos 1) es igual a c más logaritmo de (x menos 1)
- ( menos logaritmo de (u menos uno) menos cuatro) dividir por (u menos uno) es igual a c más logaritmo de (x menos uno)
- -logu-1-4/u-1=c+logx-1
- (-log(u-1)-4) dividir por (u-1)=c+log(x-1)
-
Expresiones semejantes
- (-log(u-1)+4)/(u-1)=c+log(x-1)
- (-log(u-1)-4)/(u-1)=c+log(x+1)
- (-log(u+1)-4)/(u-1)=c+log(x-1)
- (-log(u-1)-4)/(u+1)=c+log(x-1)
- log(y-1)/2-log(y+1)/2=c+log(x)-1/x
- (-log(u-1)-4)/(u-1)=c-log(x-1)
- (log(u-1)-4)/(u-1)=c+log(x-1)
-
Expresiones con funciones
- Logaritmo log
- log(5,x^(2*y))+log(e,(x+y)^5)=17
- log(x^2-x-3)=log(x)
- log(y)-3+4/y=0
- log2(2𝑥−3)=4
- log(15,(x+7)^2)=0
- Logaritmo log
- log(5,x^(2*y))+log(e,(x+y)^5)=17
- log(x^2-x-3)=log(x)
- log(y)-3+4/y=0
- log2(2𝑥−3)=4
- log(15,(x+7)^2)=0
(-log(u-1)-4)/(u-1)=c+log(x-1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
-log(u - 1) - 4
--------------- = c + log(x - 1)
u - 1
$$\frac{- \log{\left(u - 1 \right)} - 4}{u - 1} = c + \log{\left(x - 1 \right)}$$
Solución detallada
Tenemos la ecuación
$$\frac{- \log{\left(u - 1 \right)} - 4}{u - 1} = c + \log{\left(x - 1 \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \log{\left(x - 1 \right)} = c + \frac{\log{\left(u - 1 \right)} + 4}{u - 1}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =-1
$$\log{\left(x - 1 \right)} = - c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}$$
Es la ecuación de la forma:
Por definición log
entonces
$$x - 1 = e^{\frac{c + \frac{\log{\left(u - 1 \right)} + 4}{u - 1}}{-1}}$$
simplificamos
$$x - 1 = e^{- c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}}$$
$$x = e^{- c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}} + 1$$
$$\frac{- \log{\left(u - 1 \right)} - 4}{u - 1} = c + \log{\left(x - 1 \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \log{\left(x - 1 \right)} = c + \frac{\log{\left(u - 1 \right)} + 4}{u - 1}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =-1
$$\log{\left(x - 1 \right)} = - c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x - 1 = e^{\frac{c + \frac{\log{\left(u - 1 \right)} + 4}{u - 1}}{-1}}$$
simplificamos
$$x - 1 = e^{- c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}}$$
$$x = e^{- c - \frac{\log{\left(u - 1 \right)} + 4}{u - 1}} + 1$$
Gráfica
Respuesta rápida
[src]
4 log(|-1 + u|) re(c*u) re(c) 4*re(u) im(c)*im(u) re(c)*re(u) arg(-1 + u)*im(u) im(u)*im(c*u) log(|-1 + u|)*re(u) re(u)*re(c*u) 4 log(|-1 + u|) re(c*u) re(c) 4*re(u) im(c)*im(u) re(c)*re(u) arg(-1 + u)*im(u) im(u)*im(c*u) log(|-1 + u|)*re(u) re(u)*re(c*u)
----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - ----------------------------- - ----------------------------- ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - ----------------------------- - -----------------------------
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
/ arg(-1 + u) im(c*u) im(c) 4*im(u) im(c)*re(u) im(u)*log(|-1 + u|) im(u)*re(c*u) arg(-1 + u)*re(u) im(u)*re(c) im(c*u)*re(u) \ 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) / arg(-1 + u) im(c*u) im(c) 4*im(u) im(c)*re(u) im(u)*log(|-1 + u|) im(u)*re(c*u) arg(-1 + u)*re(u) im(u)*re(c) im(c*u)*re(u) \
x1 = 1 + cos|----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - -----------------------------|*e + I*e *sin|----------------------------- + ----------------------------- - ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- - ----------------------------- - ----------------------------- - -----------------------------|
| 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 | | 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
\1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u)/ \1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u) 1 + im (u) + re (u) - 2*re(u)/
$$x_{1} = i e^{- \frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\log{\left(\left|{u - 1}\right| \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c\right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{4 \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1}} \sin{\left(\frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4 \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} \right)} + e^{- \frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\log{\left(\left|{u - 1}\right| \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c\right)} \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{4 \operatorname{re}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1}} \cos{\left(\frac{\log{\left(\left|{u - 1}\right| \right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{re}{\left(u\right)} \arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{re}{\left(c u\right)} \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} - \frac{\operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{4 \operatorname{im}{\left(u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\operatorname{im}{\left(c u\right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} + \frac{\arg{\left(u - 1 \right)}}{\left(\operatorname{re}{\left(u\right)}\right)^{2} - 2 \operatorname{re}{\left(u\right)} + \left(\operatorname{im}{\left(u\right)}\right)^{2} + 1} \right)} + 1$$
x1 = i*exp(-log(|u - 1|)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + log(|u - 1|)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - 4*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4/(re(u)^2 - 2*re(u) + im(u)^2 + 1))*sin(log(|u - 1|)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(u)*im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1)) + exp(-log(|u - 1|)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + log(|u - 1|)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c)*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - 4*re(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4/(re(u)^2 - 2*re(u) + im(u)^2 + 1))*cos(log(|u - 1|)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(c)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(u)*im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - re(u)*arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + re(c*u)*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) - im(c)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + 4*im(u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + im(c*u)/(re(u)^2 - 2*re(u) + im(u)^2 + 1) + arg(u - 1)/(re(u)^2 - 2*re(u) + im(u)^2 + 1)) + 1