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3log5(x)+loga(x)-a=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
  log(x)   log(x)        
3*------ + ------ - a = 0
  log(5)   log(a)        
a+(3log(x)log(5)+log(x)log(a))=0- a + \left(3 \frac{\log{\left(x \right)}}{\log{\left(5 \right)}} + \frac{\log{\left(x \right)}}{\log{\left(a \right)}}\right) = 0
Gráfica
Respuesta rápida [src]
                                                 /     a*log(a)    \               /     a*log(a)    \                                  
                                        log(5)*re|-----------------|      log(5)*re|-----------------|                                  
        /  /     a*log(a)    \       \           \3*log(a) + log(5)/               \3*log(a) + log(5)/    /  /     a*log(a)    \       \
x1 = cos|im|-----------------|*log(5)|*e                             + I*e                            *sin|im|-----------------|*log(5)|
        \  \3*log(a) + log(5)/       /                                                                    \  \3*log(a) + log(5)/       /
x1=ielog(5)re(alog(a)3log(a)+log(5))sin(log(5)im(alog(a)3log(a)+log(5)))+elog(5)re(alog(a)3log(a)+log(5))cos(log(5)im(alog(a)3log(a)+log(5)))x_{1} = i e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \sin{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)} + e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \cos{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)}
x1 = i*exp(log(5)*re(a*log(a)/(3*log(a) + log(5))))*sin(log(5)*im(a*log(a)/(3*log(a) + log(5)))) + exp(log(5)*re(a*log(a)/(3*log(a) + log(5))))*cos(log(5)*im(a*log(a)/(3*log(a) + log(5))))
Suma y producto de raíces [src]
suma
                                            /     a*log(a)    \               /     a*log(a)    \                                  
                                   log(5)*re|-----------------|      log(5)*re|-----------------|                                  
   /  /     a*log(a)    \       \           \3*log(a) + log(5)/               \3*log(a) + log(5)/    /  /     a*log(a)    \       \
cos|im|-----------------|*log(5)|*e                             + I*e                            *sin|im|-----------------|*log(5)|
   \  \3*log(a) + log(5)/       /                                                                    \  \3*log(a) + log(5)/       /
ielog(5)re(alog(a)3log(a)+log(5))sin(log(5)im(alog(a)3log(a)+log(5)))+elog(5)re(alog(a)3log(a)+log(5))cos(log(5)im(alog(a)3log(a)+log(5)))i e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \sin{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)} + e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \cos{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)}
=
                                            /     a*log(a)    \               /     a*log(a)    \                                  
                                   log(5)*re|-----------------|      log(5)*re|-----------------|                                  
   /  /     a*log(a)    \       \           \3*log(a) + log(5)/               \3*log(a) + log(5)/    /  /     a*log(a)    \       \
cos|im|-----------------|*log(5)|*e                             + I*e                            *sin|im|-----------------|*log(5)|
   \  \3*log(a) + log(5)/       /                                                                    \  \3*log(a) + log(5)/       /
ielog(5)re(alog(a)3log(a)+log(5))sin(log(5)im(alog(a)3log(a)+log(5)))+elog(5)re(alog(a)3log(a)+log(5))cos(log(5)im(alog(a)3log(a)+log(5)))i e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \sin{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)} + e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \cos{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)}
producto
                                            /     a*log(a)    \               /     a*log(a)    \                                  
                                   log(5)*re|-----------------|      log(5)*re|-----------------|                                  
   /  /     a*log(a)    \       \           \3*log(a) + log(5)/               \3*log(a) + log(5)/    /  /     a*log(a)    \       \
cos|im|-----------------|*log(5)|*e                             + I*e                            *sin|im|-----------------|*log(5)|
   \  \3*log(a) + log(5)/       /                                                                    \  \3*log(a) + log(5)/       /
ielog(5)re(alog(a)3log(a)+log(5))sin(log(5)im(alog(a)3log(a)+log(5)))+elog(5)re(alog(a)3log(a)+log(5))cos(log(5)im(alog(a)3log(a)+log(5)))i e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \sin{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)} + e^{\log{\left(5 \right)} \operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} \cos{\left(\log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)} \right)}
=
   /     a*log(a)    \      /     a*log(a)    \       
 re|-----------------|  I*im|-----------------|*log(5)
   \3*log(a) + log(5)/      \3*log(a) + log(5)/       
5                     *e                              
5re(alog(a)3log(a)+log(5))eilog(5)im(alog(a)3log(a)+log(5))5^{\operatorname{re}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}} e^{i \log{\left(5 \right)} \operatorname{im}{\left(\frac{a \log{\left(a \right)}}{3 \log{\left(a \right)} + \log{\left(5 \right)}}\right)}}
5^re(a*log(a)/(3*log(a) + log(5)))*exp(i*im(a*log(a)/(3*log(a) + log(5)))*log(5))