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lny=ax+by la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(y) = a*x + b*y
log⁡(y)=ax+by\log{\left(y \right)} = a x + b y
Simplificar
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
log⁡(y)=ax+by\log{\left(y \right)} = a x + b y
Коэффициент при x равен
−a- a
entonces son posibles los casos para a :
a<0a < 0
a=0a = 0
Consideremos todos los casos con detalles:
Con
a<0a < 0
la ecuación será
−by+x+log⁡(y)=0- b y + x + \log{\left(y \right)} = 0
su solución
x=by−log⁡(y)x = b y - \log{\left(y \right)}
Con
a=0a = 0
la ecuación será
−by+log⁡(y)=0- 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(−(log⁡(∣y∣)−re⁡(by))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(log⁡(∣y∣)−re⁡(by))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))im⁡(a)(re⁡(a))2+(im⁡(a))2i \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(−(log⁡(∣y∣)−re⁡(by))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(log⁡(∣y∣)−re⁡(by))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))im⁡(a)(re⁡(a))2+(im⁡(a))2i \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(−(log⁡(∣y∣)−re⁡(by))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(log⁡(∣y∣)−re⁡(by))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))im⁡(a)(re⁡(a))2+(im⁡(a))2i \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)
−i((log⁡(∣y∣)−re⁡(by))im⁡(a)+(im⁡(by)−arg⁡(y))re⁡(a))+(log⁡(∣y∣)−re⁡(by))re⁡(a)−(im⁡(by)−arg⁡(y))im⁡(a)(re⁡(a))2+(im⁡(a))2\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)
x1=i(−(log⁡(∣y∣)−re⁡(by))im⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))re⁡(a)(re⁡(a))2+(im⁡(a))2)+(log⁡(∣y∣)−re⁡(by))re⁡(a)(re⁡(a))2+(im⁡(a))2+(−im⁡(by)+arg⁡(y))im⁡(a)(re⁡(a))2+(im⁡(a))2x_{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)
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