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25*4^(x*(x-3))=16*5^(2*x) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

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Solución

Ha introducido [src] 
    x*(x - 3)       2*x
25*4          = 16*5
25⋅4x(x−3)=16⋅52x25 \cdot 4^{x \left(x - 3\right)} = 16 \cdot 5^{2 x}
Simplificar
Suma y producto de raíces [src] 
suma
     _____________________________________                _____________________________________          
    /    2            2         / log(4)\                /    2            2         / log(4)\           
- \/  log (5) + 17*log (2) + log\5      /  + log(40)   \/  log (5) + 17*log (2) + log\5      /  + log(40)
---------------------------------------------------- + --------------------------------------------------
                      2*log(2)                                              2*log(2)
−log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)+log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)\frac{- \sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} + \frac{\sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} 
=
   _____________________________________                  _____________________________________          
  /    2            2         / log(4)\                  /    2            2         / log(4)\           
\/  log (5) + 17*log (2) + log\5      /  + log(40)   - \/  log (5) + 17*log (2) + log\5      /  + log(40)
-------------------------------------------------- + ----------------------------------------------------
                     2*log(2)                                              2*log(2)
−log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)+log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)\frac{- \sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} + \frac{\sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} 
producto
     _____________________________________              _____________________________________          
    /    2            2         / log(4)\              /    2            2         / log(4)\           
- \/  log (5) + 17*log (2) + log\5      /  + log(40) \/  log (5) + 17*log (2) + log\5      /  + log(40)
----------------------------------------------------*--------------------------------------------------
                      2*log(2)                                            2*log(2)
−log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)\frac{- \sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} \frac{\sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} 
=
 /   2         2             2         / log(4)\\ 
-\log (5) - log (40) + 17*log (2) + log\5      // 
--------------------------------------------------
                         2                        
                    4*log (2)
−−log⁡(40)2+log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)24log⁡(2)2- \frac{- \log{\left(40 \right)}^{2} + \log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}}{4 \log{\left(2 \right)}^{2}} 
-(log(5)^2 - log(40)^2 + 17*log(2)^2 + log(5^log(4)))/(4*log(2)^2)
Respuesta rápida [src] 
          _____________________________________          
         /    2            2         / log(4)\           
     - \/  log (5) + 17*log (2) + log\5      /  + log(40)
x1 = ----------------------------------------------------
                           2*log(2)
x1=−log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)x_{1} = \frac{- \sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} 
        _____________________________________          
       /    2            2         / log(4)\           
     \/  log (5) + 17*log (2) + log\5      /  + log(40)
x2 = --------------------------------------------------
                          2*log(2)
x2=log⁡(5log⁡(4))+log⁡(5)2+17log⁡(2)2+log⁡(40)2log⁡(2)x_{2} = \frac{\sqrt{\log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(5 \right)}^{2} + 17 \log{\left(2 \right)}^{2}} + \log{\left(40 \right)}}{2 \log{\left(2 \right)}} 
x2 = (sqrt(log(5^log(4)) + log(5)^2 + 17*log(2)^2) + log(40))/(2*log(2))
Respuesta numérica [src] 
x1 = 0.0611945255628481
x2 = 5.26073356932451
x2 = 5.26073356932451
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