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log(a-x+2)/(log(x)-1)=2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(a - x + 2)    
-------------- = 2
  log(x) - 1
log⁡((a−x)+2)log⁡(x)−1=2\frac{\log{\left(\left(a - x\right) + 2 \right)}}{\log{\left(x \right)} - 1} = 2
Simplificar
Gráfica
Respuesta rápida [src] 
       /         _________________________________                                      \           _________________________________                                      
       |        /                   2                 /     /                        2\\|          /                   2                 /     /                        2\\
       |     4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||       4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /|
     E*|-E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||   E*I*\/   \8 + 4*re(a) + e /  + 16*im (a) *sin|--------------------------------|
       \                                              \               2                //                                                \               2                /
x1 = ------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------
                                              2                                                                                    2
x1=e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)−e)2+ei(4re⁡(a)+e2+8)2+16(im⁡(a))24sin⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)2x_{1} = \frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} - e\right)}{2} + \frac{e i \sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)}}{2} 
         /        _________________________________                                      \           _________________________________                                      
         |       /                   2                 /     /                        2\\|          /                   2                 /     /                        2\\
         |    4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||       4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /|
       E*|E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||   E*I*\/   \8 + 4*re(a) + e /  + 16*im (a) *sin|--------------------------------|
         \                                             \               2                //                                                \               2                /
x2 = - ----------------------------------------------------------------------------------- - -------------------------------------------------------------------------------
                                                2                                                                                   2
x2=−e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)+e)2−ei(4re⁡(a)+e2+8)2+16(im⁡(a))24sin⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)2x_{2} = - \frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} + e\right)}{2} - \frac{e i \sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)}}{2} 
x2 = -E*(((4*re(a) + exp(2) + 8)^2 + 16*im(a)^2)^(1/4)*cos(atan2(4*im(a, 4*re(a) + exp(2) + 8)/2) + E)/2 - E*i*((4*re(a) + exp(2) + 8)^2 + 16*im(a)^2)^(1/4)*sin(atan2(4*im(a), 4*re(a) + exp(2) + 8)/2)/2)
Suma y producto de raíces [src] 
suma
  /         _________________________________                                      \           _________________________________                                             /        _________________________________                                      \           _________________________________                                      
  |        /                   2                 /     /                        2\\|          /                   2                 /     /                        2\\       |       /                   2                 /     /                        2\\|          /                   2                 /     /                        2\\
  |     4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||       4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /|       |    4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||       4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /|
E*|-E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||   E*I*\/   \8 + 4*re(a) + e /  + 16*im (a) *sin|--------------------------------|     E*|E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||   E*I*\/   \8 + 4*re(a) + e /  + 16*im (a) *sin|--------------------------------|
  \                                              \               2                //                                                \               2                /       \                                             \               2                //                                                \               2                /
------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------- + - ----------------------------------------------------------------------------------- - -------------------------------------------------------------------------------
                                         2                                                                                    2                                                                                     2                                                                                   2
(e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)−e)2+ei(4re⁡(a)+e2+8)2+16(im⁡(a))24sin⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)2)+(−e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)+e)2−ei(4re⁡(a)+e2+8)2+16(im⁡(a))24sin⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)2)\left(\frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} - e\right)}{2} + \frac{e i \sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)}}{2}\right) + \left(- \frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} + e\right)}{2} - \frac{e i \sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)}}{2}\right) 
=
  /         _________________________________                                      \     /        _________________________________                                      \
  |        /                   2                 /     /                        2\\|     |       /                   2                 /     /                        2\\|
  |     4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||     |    4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||
E*|-E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||   E*|E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||
  \                                              \               2                //     \                                             \               2                //
------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------
                                         2                                                                                      2
e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)−e)2−e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)+e)2\frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} - e\right)}{2} - \frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} + e\right)}{2} 
producto
/  /         _________________________________                                      \           _________________________________                                      \ /    /        _________________________________                                      \           _________________________________                                      \
|  |        /                   2                 /     /                        2\\|          /                   2                 /     /                        2\\| |    |       /                   2                 /     /                        2\\|          /                   2                 /     /                        2\\|
|  |     4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||       4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /|| |    |    4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||       4 /  /               2\         2        |atan2\4*im(a), 8 + 4*re(a) + e /||
|E*|-E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||   E*I*\/   \8 + 4*re(a) + e /  + 16*im (a) *sin|--------------------------------|| |  E*|E + \/   \8 + 4*re(a) + e /  + 16*im (a) *cos|--------------------------------||   E*I*\/   \8 + 4*re(a) + e /  + 16*im (a) *sin|--------------------------------||
|  \                                              \               2                //                                                \               2                /| |    \                                             \               2                //                                                \               2                /|
|------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------|*|- ----------------------------------------------------------------------------------- - -------------------------------------------------------------------------------|
\                                         2                                                                                    2                                       / \                                           2                                                                                   2                                       /
(e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)−e)2+ei(4re⁡(a)+e2+8)2+16(im⁡(a))24sin⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)2)(−e((4re⁡(a)+e2+8)2+16(im⁡(a))24cos⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)+e)2−ei(4re⁡(a)+e2+8)2+16(im⁡(a))24sin⁡(atan2⁡(4im⁡(a),4re⁡(a)+e2+8)2)2)\left(\frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} - e\right)}{2} + \frac{e i \sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)}}{2}\right) \left(- \frac{e \left(\sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)} + e\right)}{2} - \frac{e i \sqrt[4]{\left(4 \operatorname{re}{\left(a\right)} + e^{2} + 8\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(a\right)},4 \operatorname{re}{\left(a\right)} + e^{2} + 8 \right)}}{2} \right)}}{2}\right) 
=
                        2
-(2 + I*im(a) + re(a))*e
−(re⁡(a)+iim⁡(a)+2)e2- \left(\operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} + 2\right) e^{2} 
-(2 + i*im(a) + re(a))*exp(2)
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