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Otras calculadoras
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- La ecuación:
-
Ecuación x^3-x^2-x-1=0
-
Ecuación 3x-2(3x+4)=10
-
Ecuación 12-4(x-3)=39-9x
-
Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- 7*x-1*y=0
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- Integral de d{x}:
- lny
- Derivada de:
-
lny
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Expresiones idénticas
- lny=ax+by
- lny es igual a ax más by
-
Expresiones semejantes
- a*x+b*y+c=0
- a*x+b*y-82/9=0
- 0.5ln(y)=-ln(x+1)
- lny=ax-by
- ln(y)+y*x^3+x^4
- (y^2)-5y=log(y)+ln(y)
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Expresiones con funciones
- lny
- lny=-2ln(x^2+1)+const
- lny=(-1/x)+lnc
- lny+(x/y)^0.5=2
- ax
- ax+b=c
- ax=4a+14∣x∣+2x−x2
- ax+by+c=0
- ax=-by-c
- ax=2a-1
lny=ax+by la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$\log{\left(y \right)} = a x + b y$$
Коэффициент при x равен
$$- a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- b y + x + \log{\left(y \right)} = 0$$
su solución
$$x = b y - \log{\left(y \right)}$$
Con
$$a = 0$$
la ecuación será
$$- b y + \log{\left(y \right)} = 0$$
su solución
$$\log{\left(y \right)} = a x + b y$$
Коэффициент при x равен
$$- a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- b y + x + \log{\left(y \right)} = 0$$
su solución
$$x = b y - \log{\left(y \right)}$$
Con
$$a = 0$$
la ecuación será
$$- b y + \log{\left(y \right)} = 0$$
su solución
Gráfica
Suma y producto de raíces
[src]
suma
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a) I*|------------------------- - ---------------------------| + ------------------------- + --------------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a) I*|------------------------- - ---------------------------| + ------------------------- + --------------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a) I*|------------------------- - ---------------------------| + ------------------------- + --------------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
(-re(b*y) + log(|y|))*re(a) - I*((-arg(y) + im(b*y))*re(a) + (-re(b*y) + log(|y|))*im(a)) - (-arg(y) + im(b*y))*im(a)
---------------------------------------------------------------------------------------------------------------------
2 2
im (a) + re (a)
$$\frac{- i \left(\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)} + \left(\operatorname{im}{\left(b y\right)} - \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}\right) + \left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(b y\right)} - \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
((-re(b*y) + log(|y|))*re(a) - i*((-arg(y) + im(b*y))*re(a) + (-re(b*y) + log(|y|))*im(a)) - (-arg(y) + im(b*y))*im(a))/(im(a)^2 + re(a)^2)
Respuesta rápida
[src]
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a)
x1 = I*|------------------------- - ---------------------------| + ------------------------- + ---------------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$x_{1} = i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = i*(-(log(|y|) - re(b*y))*im(a)/(re(a)^2 + im(a)^2) + (-im(b*y) + arg(y))*re(a)/(re(a)^2 + im(a)^2)) + (log(|y|) - re(b*y))*re(a)/(re(a)^2 + im(a)^2) + (-im(b*y) + arg(y))*im(a)/(re(a)^2 + im(a)^2)