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(5x-4)*3^(4x-5)=5x-4 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
           4*x - 5          
(5*x - 4)*3        = 5*x - 4
34x−5(5x−4)=5x−43^{4 x - 5} \left(5 x - 4\right) = 5 x - 4
Simplificar
Gráfica
02468-8-6-4-210-5000000000000000000001e21
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 4/5
x1=45x_{1} = \frac{4}{5} 
x2 = 5/4
x2=54x_{2} = \frac{5}{4} 
     log(243)    pi*I 
x3 = -------- + ------
     4*log(3)   log(3)
x3=log⁡(243)4log⁡(3)+iπlog⁡(3)x_{3} = \frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}} 
     log(243)     pi*I  
x4 = -------- - --------
     4*log(3)   2*log(3)
x4=log⁡(243)4log⁡(3)−iπ2log⁡(3)x_{4} = \frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} - \frac{i \pi}{2 \log{\left(3 \right)}} 
     log(243)     pi*I  
x5 = -------- + --------
     4*log(3)   2*log(3)
x5=log⁡(243)4log⁡(3)+iπ2log⁡(3)x_{5} = \frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} + \frac{i \pi}{2 \log{\left(3 \right)}} 
x5 = log(243)/(4*log(3)) + i*pi/(2*log(3))
Suma y producto de raíces [src] 
suma
            log(243)    pi*I    log(243)     pi*I     log(243)     pi*I  
4/5 + 5/4 + -------- + ------ + -------- - -------- + -------- + --------
            4*log(3)   log(3)   4*log(3)   2*log(3)   4*log(3)   2*log(3)
(log⁡(243)4log⁡(3)+iπ2log⁡(3))+((log⁡(243)4log⁡(3)−iπ2log⁡(3))+((45+54)+(log⁡(243)4log⁡(3)+iπlog⁡(3))))\left(\frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} + \frac{i \pi}{2 \log{\left(3 \right)}}\right) + \left(\left(\frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} - \frac{i \pi}{2 \log{\left(3 \right)}}\right) + \left(\left(\frac{4}{5} + \frac{5}{4}\right) + \left(\frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}}\right)\right)\right) 
=
41   3*log(243)    pi*I 
-- + ---------- + ------
20    4*log(3)    log(3)
4120+3log⁡(243)4log⁡(3)+iπlog⁡(3)\frac{41}{20} + \frac{3 \log{\left(243 \right)}}{4 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}} 
producto
4*5 /log(243)    pi*I \ /log(243)     pi*I  \ /log(243)     pi*I  \
---*|-------- + ------|*|-------- - --------|*|-------- + --------|
5*4 \4*log(3)   log(3)/ \4*log(3)   2*log(3)/ \4*log(3)   2*log(3)/
4⋅54⋅5(log⁡(243)4log⁡(3)+iπlog⁡(3))(log⁡(243)4log⁡(3)−iπ2log⁡(3))(log⁡(243)4log⁡(3)+iπ2log⁡(3))\frac{4 \cdot 5}{4 \cdot 5} \left(\frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}}\right) \left(\frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} - \frac{i \pi}{2 \log{\left(3 \right)}}\right) \left(\frac{\log{\left(243 \right)}}{4 \log{\left(3 \right)}} + \frac{i \pi}{2 \log{\left(3 \right)}}\right) 
=
(-2*pi*I + log(243))*(2*pi*I + log(243))*(4*pi*I + log(243))
------------------------------------------------------------
                               3                            
                         64*log (3)
(log⁡(243)−2iπ)(log⁡(243)+2iπ)(log⁡(243)+4iπ)64log⁡(3)3\frac{\left(\log{\left(243 \right)} - 2 i \pi\right) \left(\log{\left(243 \right)} + 2 i \pi\right) \left(\log{\left(243 \right)} + 4 i \pi\right)}{64 \log{\left(3 \right)}^{3}} 
(-2*pi*i + log(243))*(2*pi*i + log(243))*(4*pi*i + log(243))/(64*log(3)^3)
Respuesta numérica [src] 
x1 = 0.8
x2 = 1.25
x3 = 1.25 + 2.85960086738013*i
x4 = 1.25 - 1.42980043369006*i
x5 = 1.25 + 1.42980043369006*i
x5 = 1.25 + 1.42980043369006*i
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