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log(10,x)^2+log(10,x^2)=log(10,2)-1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
         2                          
/log(10)\    log(10)                
|-------|  + ------- = log(51/5) - 1
\ log(x)/       / 2\                
             log\x /
(log⁡(10)log⁡(x))2+log⁡(10)log⁡(x2)=−1+log⁡(515)\left(\frac{\log{\left(10 \right)}}{\log{\left(x \right)}}\right)^{2} + \frac{\log{\left(10 \right)}}{\log{\left(x^{2} \right)}} = -1 + \log{\left(\frac{51}{5} \right)}
Simplificar
Gráfica
05-10-51015202530-200200
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
                _________________________________________
               /          /2094704750199298376445300801\ 
       -1 +   /  -15 + log|----------------------------| 
            \/            \        152587890625        / 
       --------------------------------------------------
                       4*(1 + log(5/51))                 
x1 = 10
x1=10−1+−15+log⁡(2094704750199298376445300801152587890625)4(log⁡(551)+1)x_{1} = 10^{\frac{-1 + \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}}}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}} 
                _________________________________________
               /          /2094704750199298376445300801\ 
       -1 -   /  -15 + log|----------------------------| 
            \/            \        152587890625        / 
       --------------------------------------------------
                       4*(1 + log(5/51))                 
x2 = 10
x2=10−−15+log⁡(2094704750199298376445300801152587890625)−14(log⁡(551)+1)x_{2} = 10^{\frac{- \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}} - 1}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}} 
x2 = 10^((-sqrt(-15 + log(2094704750199298376445300801/152587890625)) - 1)/(4*(log(5/51) + 1)))
Suma y producto de raíces [src] 
suma
           _________________________________________              _________________________________________
          /          /2094704750199298376445300801\              /          /2094704750199298376445300801\ 
  -1 +   /  -15 + log|----------------------------|      -1 -   /  -15 + log|----------------------------| 
       \/            \        152587890625        /           \/            \        152587890625        / 
  --------------------------------------------------     --------------------------------------------------
                  4*(1 + log(5/51))                                      4*(1 + log(5/51))                 
10                                                   + 10
10−1+−15+log⁡(2094704750199298376445300801152587890625)4(log⁡(551)+1)+10−−15+log⁡(2094704750199298376445300801152587890625)−14(log⁡(551)+1)10^{\frac{-1 + \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}}}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}} + 10^{\frac{- \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}} - 1}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}} 
=
           _________________________________________              _________________________________________
          /          /2094704750199298376445300801\              /          /2094704750199298376445300801\ 
  -1 +   /  -15 + log|----------------------------|      -1 -   /  -15 + log|----------------------------| 
       \/            \        152587890625        /           \/            \        152587890625        / 
  --------------------------------------------------     --------------------------------------------------
                  4*(1 + log(5/51))                                      4*(1 + log(5/51))                 
10                                                   + 10
10−1+−15+log⁡(2094704750199298376445300801152587890625)4(log⁡(551)+1)+10−−15+log⁡(2094704750199298376445300801152587890625)−14(log⁡(551)+1)10^{\frac{-1 + \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}}}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}} + 10^{\frac{- \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}} - 1}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}} 
producto
           _________________________________________            _________________________________________
          /          /2094704750199298376445300801\            /          /2094704750199298376445300801\ 
  -1 +   /  -15 + log|----------------------------|    -1 -   /  -15 + log|----------------------------| 
       \/            \        152587890625        /         \/            \        152587890625        / 
  --------------------------------------------------   --------------------------------------------------
                  4*(1 + log(5/51))                                    4*(1 + log(5/51))                 
10                                                  *10
10−−15+log⁡(2094704750199298376445300801152587890625)−14(log⁡(551)+1)10−−1+−15+log⁡(2094704750199298376445300801152587890625)4(log⁡(551)+1)\frac{10^{\frac{- \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}} - 1}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}}}{10^{- \frac{-1 + \sqrt{-15 + \log{\left(\frac{2094704750199298376445300801}{152587890625} \right)}}}{4 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}}} 
=
         -1        
  -----------------
  2*(1 + log(5/51))
10
10−12(log⁡(551)+1)10^{- \frac{1}{2 \left(\log{\left(\frac{5}{51} \right)} + 1\right)}} 
10^(-1/(2*(1 + log(5/51))))
Respuesta numérica [src] 
x1 = 0.199130174837955
x2 = -1.86186250278971 + 0.135048098096965*i
x3 = 11.994077741522
x3 = 11.994077741522
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