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log(x+5,5)-log(x+3,5)+log(x+1,5)=1+log(0,6,5) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                                                  log(3/5)
log(x + 11/2) - log(x + 7/2) + log(x + 3/2) = 1 + --------
                                                   log(5)
(−log⁡(x+72)+log⁡(x+112))+log⁡(x+32)=log⁡(35)log⁡(5)+1\left(- \log{\left(x + \frac{7}{2} \right)} + \log{\left(x + \frac{11}{2} \right)}\right) + \log{\left(x + \frac{3}{2} \right)} = \frac{\log{\left(\frac{3}{5} \right)}}{\log{\left(5 \right)}} + 1
Simplificar
Gráfica
05-20-15-10-510-2020
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                     ______________                        ______________
         1          /         2                1          /         2    
       ------      /        ------           ------      /        ------ 
       log(5)     /         log(5)           log(5)     /         log(5) 
  7   3         \/    16 + 3            7   3         \/    16 + 3       
- - + ------- + ------------------- + - - + ------- - -------------------
  2      2               2              2      2               2
(−72−32log⁡(5)+162+31log⁡(5)2)+(−72+31log⁡(5)2+32log⁡(5)+162)\left(- \frac{7}{2} - \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2}\right) + \left(- \frac{7}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2} + \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2}\right) 
=
        1   
      ------
      log(5)
-7 + 3
−7+31log⁡(5)-7 + 3^{\frac{1}{\log{\left(5 \right)}}} 
producto
/                     ______________\ /                     ______________\
|         1          /         2    | |         1          /         2    |
|       ------      /        ------ | |       ------      /        ------ |
|       log(5)     /         log(5) | |       log(5)     /         log(5) |
|  7   3         \/    16 + 3       | |  7   3         \/    16 + 3       |
|- - + ------- + -------------------|*|- - + ------- - -------------------|
\  2      2               2         / \  2      2               2         /
(−72+31log⁡(5)2+32log⁡(5)+162)(−72−32log⁡(5)+162+31log⁡(5)2)\left(- \frac{7}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2} + \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2}\right) \left(- \frac{7}{2} - \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2}\right) 
=
          1   
        ------
        log(5)
33   7*3      
-- - ---------
4        2
334−7⋅31log⁡(5)2\frac{33}{4} - \frac{7 \cdot 3^{\frac{1}{\log{\left(5 \right)}}}}{2} 
33/4 - 7*3^(1/log(5))/2
Respuesta rápida [src] 
                          ______________
              1          /         2    
            ------      /        ------ 
            log(5)     /         log(5) 
       7   3         \/    16 + 3       
x1 = - - + ------- + -------------------
       2      2               2
x1=−72+31log⁡(5)2+32log⁡(5)+162x_{1} = - \frac{7}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2} + \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2} 
                          ______________
              1          /         2    
            ------      /        ------ 
            log(5)     /         log(5) 
       7   3         \/    16 + 3       
x2 = - - + ------- - -------------------
       2      2               2
x2=−72−32log⁡(5)+162+31log⁡(5)2x_{2} = - \frac{7}{2} - \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2} 
x2 = -7/2 - sqrt(3^(2/log(5)) + 16)/2 + 3^(1/log(5))/2
Respuesta numérica [src] 
x1 = -4.74188399760631
x2 = -0.279087251538907
x2 = -0.279087251538907
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