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f*(x)=(log(x+3)/log(3)) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
      log(x + 3)
f*x = ----------
        log(3)
fx=log⁡(x+3)log⁡(3)f x = \frac{\log{\left(x + 3 \right)}}{\log{\left(3 \right)}}
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
  //                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      \   /                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      
  |\log(27)*re(f) + re\W\-f*e          *log(3)///*im(f)   \im(f)*log(27) + im\W\-f*e          *log(3)///*re(f)|   \im(f)*log(27) + im\W\-f*e          *log(3)///*im(f)   \log(27)*re(f) + re\W\-f*e          *log(3)///*re(f)
I*|---------------------------------------------------- - ----------------------------------------------------| - ---------------------------------------------------- - ----------------------------------------------------
  |              /  2        2   \                                      /  2        2   \                     |                 /  2        2   \                                      /  2        2   \                     
  \              \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)              /                 \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)
−(log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)+i((log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3))- \frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} + i \left(\frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}}\right) 
=
  //                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      \   /                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      
  |\log(27)*re(f) + re\W\-f*e          *log(3)///*im(f)   \im(f)*log(27) + im\W\-f*e          *log(3)///*re(f)|   \im(f)*log(27) + im\W\-f*e          *log(3)///*im(f)   \log(27)*re(f) + re\W\-f*e          *log(3)///*re(f)
I*|---------------------------------------------------- - ----------------------------------------------------| - ---------------------------------------------------- - ----------------------------------------------------
  |              /  2        2   \                                      /  2        2   \                     |                 /  2        2   \                                      /  2        2   \                     
  \              \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)              /                 \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)
−(log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)+i((log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3))- \frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} + i \left(\frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}}\right) 
producto
  //                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      \   /                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      
  |\log(27)*re(f) + re\W\-f*e          *log(3)///*im(f)   \im(f)*log(27) + im\W\-f*e          *log(3)///*re(f)|   \im(f)*log(27) + im\W\-f*e          *log(3)///*im(f)   \log(27)*re(f) + re\W\-f*e          *log(3)///*re(f)
I*|---------------------------------------------------- - ----------------------------------------------------| - ---------------------------------------------------- - ----------------------------------------------------
  |              /  2        2   \                                      /  2        2   \                     |                 /  2        2   \                                      /  2        2   \                     
  \              \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)              /                 \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)
−(log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)+i((log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3))- \frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} + i \left(\frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}}\right) 
=
  //   /  re(f)\     / /    -f*log(27)       \\\         /  / /    -f*log(27)       \\      /  im(f)\\      \   /  / /    -f*log(27)       \\      /  im(f)\\         /   /  re(f)\     / /    -f*log(27)       \\\      
I*\\log\27     / + re\W\-f*e          *log(3)///*im(f) - \im\W\-f*e          *log(3)// + log\27     //*re(f)/ - \im\W\-f*e          *log(3)// + log\27     //*im(f) - \log\27     / + re\W\-f*e          *log(3)///*re(f)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 /  2        2   \                                                                                                       
                                                                                                 \im (f) + re (f)/*log(3)
i((log⁡(27re⁡(f))+re⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)−(log⁡(27im⁡(f))+im⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f))−(log⁡(27re⁡(f))+re⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)−(log⁡(27im⁡(f))+im⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)\frac{i \left(\left(\log{\left(27^{\operatorname{re}{\left(f\right)}} \right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)} - \left(\log{\left(27^{\operatorname{im}{\left(f\right)}} \right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}\right) - \left(\log{\left(27^{\operatorname{re}{\left(f\right)}} \right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)} - \left(\log{\left(27^{\operatorname{im}{\left(f\right)}} \right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} 
(i*((log(27^re(f)) + re(LambertW(-f*exp(-f*log(27))*log(3))))*im(f) - (im(LambertW(-f*exp(-f*log(27))*log(3))) + log(27^im(f)))*re(f)) - (im(LambertW(-f*exp(-f*log(27))*log(3))) + log(27^im(f)))*im(f) - (log(27^re(f)) + re(LambertW(-f*exp(-f*log(27))*log(3))))*re(f))/((im(f)^2 + re(f)^2)*log(3))
Respuesta rápida [src] 
       //                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      \   /                  / /    -f*log(27)       \\\         /                  / /    -f*log(27)       \\\      
       |\log(27)*re(f) + re\W\-f*e          *log(3)///*im(f)   \im(f)*log(27) + im\W\-f*e          *log(3)///*re(f)|   \im(f)*log(27) + im\W\-f*e          *log(3)///*im(f)   \log(27)*re(f) + re\W\-f*e          *log(3)///*re(f)
x1 = I*|---------------------------------------------------- - ----------------------------------------------------| - ---------------------------------------------------- - ----------------------------------------------------
       |              /  2        2   \                                      /  2        2   \                     |                 /  2        2   \                                      /  2        2   \                     
       \              \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)              /                 \im (f) + re (f)/*log(3)                               \im (f) + re (f)/*log(3)
x1=−(log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)+i((log⁡(27)re⁡(f)+re⁡(W(−fe−flog⁡(27)log⁡(3))))im⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3)−(log⁡(27)im⁡(f)+im⁡(W(−fe−flog⁡(27)log⁡(3))))re⁡(f)((re⁡(f))2+(im⁡(f))2)log⁡(3))x_{1} = - \frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} + i \left(\frac{\left(\log{\left(27 \right)} \operatorname{re}{\left(f\right)} + \operatorname{re}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{im}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}} - \frac{\left(\log{\left(27 \right)} \operatorname{im}{\left(f\right)} + \operatorname{im}{\left(W\left(- f e^{- f \log{\left(27 \right)}} \log{\left(3 \right)}\right)\right)}\right) \operatorname{re}{\left(f\right)}}{\left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \log{\left(3 \right)}}\right) 
x1 = -(log(27)*re(f) + re(LambertW(-f*exp(-f*log(27))*log(3))))*re(f)/((re(f)^2 + im(f)^2)*log(3)) - (log(27)*im(f) + im(LambertW(-f*exp(-f*log(27))*log(3))))*im(f)/((re(f)^2 + im(f)^2)*log(3)) + i*((log(27)*re(f) + re(LambertW(-f*exp(-f*log(27))*log(3))))*im(f)/((re(f)^2 + im(f)^2)*log(3)) - (log(27)*im(f) + im(LambertW(-f*exp(-f*log(27))*log(3))))*re(f)/((re(f)^2 + im(f)^2)*log(3)))
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