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logax=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(a*x) = 0
log⁡(ax)=0\log{\left(a x \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
log⁡(ax)=0\log{\left(a x \right)} = 0
log⁡(ax)=0\log{\left(a x \right)} = 0
Es la ecuación de la forma:
log(v)=p

Por definición log
v=e^p

entonces
ax=e01a x = e^{\frac{0}{1}}
simplificamos
ax=1a x = 1
x=1ax = \frac{1}{a}
Gráfica
Suma y producto de raíces [src] 
suma
     re(a)            I*im(a)    
--------------- - ---------------
  2        2        2        2   
im (a) + re (a)   im (a) + re (a)
re⁡(a)(re⁡(a))2+(im⁡(a))2−iim⁡(a)(re⁡(a))2+(im⁡(a))2\frac{\operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
=
     re(a)            I*im(a)    
--------------- - ---------------
  2        2        2        2   
im (a) + re (a)   im (a) + re (a)
re⁡(a)(re⁡(a))2+(im⁡(a))2−iim⁡(a)(re⁡(a))2+(im⁡(a))2\frac{\operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
producto
     re(a)            I*im(a)    
--------------- - ---------------
  2        2        2        2   
im (a) + re (a)   im (a) + re (a)
re⁡(a)(re⁡(a))2+(im⁡(a))2−iim⁡(a)(re⁡(a))2+(im⁡(a))2\frac{\operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
=
-I*im(a) + re(a)
----------------
  2        2    
im (a) + re (a)
re⁡(a)−iim⁡(a)(re⁡(a))2+(im⁡(a))2\frac{\operatorname{re}{\left(a\right)} - i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
(-i*im(a) + re(a))/(im(a)^2 + re(a)^2)
Respuesta rápida [src] 
          re(a)            I*im(a)    
x1 = --------------- - ---------------
       2        2        2        2   
     im (a) + re (a)   im (a) + re (a)
x1=re⁡(a)(re⁡(a))2+(im⁡(a))2−iim⁡(a)(re⁡(a))2+(im⁡(a))2x_{1} = \frac{\operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} 
x1 = re(a)/(re(a)^2 + im(a)^2) - i*im(a)/(re(a)^2 + im(a)^2)
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