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3log8^2(3x+79)-14log8(3x+79)+18=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2                    log(3*x + 79)         
3*log (8)*(3*x + 79) - 14*------------- + 18 = 0
                              log(8)
((3x+79)3log⁡(8)2−14log⁡(3x+79)log⁡(8))+18=0\left(\left(3 x + 79\right) 3 \log{\left(8 \right)}^{2} - 14 \frac{\log{\left(3 x + 79 \right)}}{\log{\left(8 \right)}}\right) + 18 = 0
Simplificar
Respuesta rápida [src] 
                 / /                                                                                                                                                                                      3   \\          / /                                                                                                                                                                                      3   \\
                 | |                                                                                                                                                               2             -6399*log (2)||          | |                                                                                                                                                               2             -6399*log (2)||
                 | |                                                                                                                                                            log (2)          -------------||          | |                                                                                                                                                            log (2)          -------------||
                 | |      6/7 /                                                                                                                                           14___\           3           14     ||          | |      6/7 /                                                                                                                                           14___\           3           14     ||
                 | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||          | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||
            14*re|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||   14*I*im|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
       79        \ \                                                                                            7                                                                                             //          \ \                                                                                            7                                                                                             //
x1 = - -- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       3                                                                                                       3                                                                                                                                                                                                       3                                                                                                 
                                                                                                        243*log (2)                                                                                                                                                                                             243*log (2)
x1=−793−14re⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3−14iim⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3x_{1} = - \frac{79}{3} - \frac{14 \operatorname{re}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} - \frac{14 i \operatorname{im}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} 
x1 = -79/3 - 14*re(LambertW(-324*2^(6/7)*(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*2^(1/14))^(log(2)^2)*exp(-6399*log(2)^3/14)*log(2)^3/7))/(243*log(2)^3) - 14*i*im(LambertW(-324*2^(6/7)*(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*2^(1/14))^(log(2)^2)*exp(-6399*log(2)^3/14)*log(2)^3/7))/(243*log(2)^3)
Suma y producto de raíces [src] 
suma
            / /                                                                                                                                                                                      3   \\          / /                                                                                                                                                                                      3   \\
            | |                                                                                                                                                               2             -6399*log (2)||          | |                                                                                                                                                               2             -6399*log (2)||
            | |                                                                                                                                                            log (2)          -------------||          | |                                                                                                                                                            log (2)          -------------||
            | |      6/7 /                                                                                                                                           14___\           3           14     ||          | |      6/7 /                                                                                                                                           14___\           3           14     ||
            | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||          | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||
       14*re|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||   14*I*im|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
  79        \ \                                                                                            7                                                                                             //          \ \                                                                                            7                                                                                             //
- -- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  3                                                                                                       3                                                                                                                                                                                                       3                                                                                                 
                                                                                                   243*log (2)                                                                                                                                                                                             243*log (2)
−793−14re⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3−14iim⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3- \frac{79}{3} - \frac{14 \operatorname{re}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} - \frac{14 i \operatorname{im}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} 
=
            / /                                                                                                                                                                                      3   \\          / /                                                                                                                                                                                      3   \\
            | |                                                                                                                                                               2             -6399*log (2)||          | |                                                                                                                                                               2             -6399*log (2)||
            | |                                                                                                                                                            log (2)          -------------||          | |                                                                                                                                                            log (2)          -------------||
            | |      6/7 /                                                                                                                                           14___\           3           14     ||          | |      6/7 /                                                                                                                                           14___\           3           14     ||
            | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||          | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||
       14*re|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||   14*I*im|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
  79        \ \                                                                                            7                                                                                             //          \ \                                                                                            7                                                                                             //
- -- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  3                                                                                                       3                                                                                                                                                                                                       3                                                                                                 
                                                                                                   243*log (2)                                                                                                                                                                                             243*log (2)
−793−14re⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3−14iim⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3- \frac{79}{3} - \frac{14 \operatorname{re}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} - \frac{14 i \operatorname{im}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} 
producto
            / /                                                                                                                                                                                      3   \\          / /                                                                                                                                                                                      3   \\
            | |                                                                                                                                                               2             -6399*log (2)||          | |                                                                                                                                                               2             -6399*log (2)||
            | |                                                                                                                                                            log (2)          -------------||          | |                                                                                                                                                            log (2)          -------------||
            | |      6/7 /                                                                                                                                           14___\           3           14     ||          | |      6/7 /                                                                                                                                           14___\           3           14     ||
            | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||          | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||
       14*re|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||   14*I*im|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
  79        \ \                                                                                            7                                                                                             //          \ \                                                                                            7                                                                                             //
- -- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  3                                                                                                       3                                                                                                                                                                                                       3                                                                                                 
                                                                                                   243*log (2)                                                                                                                                                                                             243*log (2)
−793−14re⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3−14iim⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3- \frac{79}{3} - \frac{14 \operatorname{re}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} - \frac{14 i \operatorname{im}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} 
=
 /     / /                                                                                                                                                                                      3   \\                         / /                                                                                                                                                                                      3   \\\ 
 |     | |                                                                                                                                                               2             -6399*log (2)||                         | |                                                                                                                                                               2             -6399*log (2)||| 
 |     | |                                                                                                                                                            log (2)          -------------||                         | |                                                                                                                                                            log (2)          -------------||| 
 |     | |      6/7 /                                                                                                                                           14___\           3           14     ||                         | |      6/7 /                                                                                                                                           14___\           3           14     ||| 
 |     | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||           3             | |-324*2   *\372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*\/ 2 /       *log (2)*e             ||| 
-|14*re|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| + 6399*log (2) + 14*I*im|W|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||| 
 \     \ \                                                                                            7                                                                                             //                         \ \                                                                                            7                                                                                             /// 
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                 3                                                                                                                                                                                                              
                                                                                                                                                                                                          243*log (2)
−14re⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))+6399log⁡(2)3+14iim⁡(W(−324⋅267(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872214)log⁡(2)2log⁡(2)37e6399log⁡(2)314))243log⁡(2)3- \frac{14 \operatorname{re}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)} + 6399 \log{\left(2 \right)}^{3} + 14 i \operatorname{im}{\left(W\left(- \frac{324 \cdot 2^{\frac{6}{7}} \left(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872 \sqrt[14]{2}\right)^{\log{\left(2 \right)}^{2}} \log{\left(2 \right)}^{3}}{7 e^{\frac{6399 \log{\left(2 \right)}^{3}}{14}}}\right)\right)}}{243 \log{\left(2 \right)}^{3}} 
-(14*re(LambertW(-324*2^(6/7)*(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*2^(1/14))^(log(2)^2)*log(2)^3*exp(-6399*log(2)^3/14)/7)) + 6399*log(2)^3 + 14*i*im(LambertW(-324*2^(6/7)*(372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872*2^(1/14))^(log(2)^2)*log(2)^3*exp(-6399*log(2)^3/14)/7)))/(243*log(2)^3)
Respuesta numérica [src] 
x1 = -26.709162638942 + 0.401837369428615*i
x1 = -26.709162638942 + 0.401837369428615*i
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