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log(9^x+9a^3)/log(3)=x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   / x      3\    
log\9  + 9*a /    
-------------- = x
    log(3)
log⁡(9x+9a3)log⁡(3)=x\frac{\log{\left(9^{x} + 9 a^{3} \right)}}{\log{\left(3 \right)}} = x
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
   /|       ___________|\                                  /|       ___________|\                            
   ||      /         3 ||                                  ||      /         3 ||                            
   ||1   \/  1 - 36*a  ||        /       ___________\      ||1   \/  1 - 36*a  ||        /       ___________\
log||- - --------------||        |      /         3 |   log||- + --------------||        |      /         3 |
   \|2         2       |/   I*arg\1 - \/  1 - 36*a  /      \|2         2       |/   I*arg\1 + \/  1 - 36*a  /
------------------------- + ------------------------- + ------------------------- + -------------------------
          log(3)                      log(3)                      log(3)                      log(3)
(log⁡(∣12−1−36a32∣)log⁡(3)+iarg⁡(1−1−36a3)log⁡(3))+(log⁡(∣1−36a32+12∣)log⁡(3)+iarg⁡(1−36a3+1)log⁡(3))\left(\frac{\log{\left(\left|{\frac{1}{2} - \frac{\sqrt{1 - 36 a^{3}}}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(1 - \sqrt{1 - 36 a^{3}} \right)}}{\log{\left(3 \right)}}\right) + \left(\frac{\log{\left(\left|{\frac{\sqrt{1 - 36 a^{3}}}{2} + \frac{1}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(\sqrt{1 - 36 a^{3}} + 1 \right)}}{\log{\left(3 \right)}}\right) 
=
   /|       ___________|\      /|       ___________|\                                                        
   ||      /         3 ||      ||      /         3 ||                                                        
   ||1   \/  1 - 36*a  ||      ||1   \/  1 - 36*a  ||        /       ___________\        /       ___________\
log||- + --------------||   log||- - --------------||        |      /         3 |        |      /         3 |
   \|2         2       |/      \|2         2       |/   I*arg\1 + \/  1 - 36*a  /   I*arg\1 - \/  1 - 36*a  /
------------------------- + ------------------------- + ------------------------- + -------------------------
          log(3)                      log(3)                      log(3)                      log(3)
log⁡(∣12−1−36a32∣)log⁡(3)+log⁡(∣1−36a32+12∣)log⁡(3)+iarg⁡(1−1−36a3)log⁡(3)+iarg⁡(1−36a3+1)log⁡(3)\frac{\log{\left(\left|{\frac{1}{2} - \frac{\sqrt{1 - 36 a^{3}}}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{\log{\left(\left|{\frac{\sqrt{1 - 36 a^{3}}}{2} + \frac{1}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(1 - \sqrt{1 - 36 a^{3}} \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(\sqrt{1 - 36 a^{3}} + 1 \right)}}{\log{\left(3 \right)}} 
producto
/   /|       ___________|\                            \ /   /|       ___________|\                            \
|   ||      /         3 ||                            | |   ||      /         3 ||                            |
|   ||1   \/  1 - 36*a  ||        /       ___________\| |   ||1   \/  1 - 36*a  ||        /       ___________\|
|log||- - --------------||        |      /         3 || |log||- + --------------||        |      /         3 ||
|   \|2         2       |/   I*arg\1 - \/  1 - 36*a  /| |   \|2         2       |/   I*arg\1 + \/  1 - 36*a  /|
|------------------------- + -------------------------|*|------------------------- + -------------------------|
\          log(3)                      log(3)         / \          log(3)                      log(3)         /
(log⁡(∣12−1−36a32∣)log⁡(3)+iarg⁡(1−1−36a3)log⁡(3))(log⁡(∣1−36a32+12∣)log⁡(3)+iarg⁡(1−36a3+1)log⁡(3))\left(\frac{\log{\left(\left|{\frac{1}{2} - \frac{\sqrt{1 - 36 a^{3}}}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(1 - \sqrt{1 - 36 a^{3}} \right)}}{\log{\left(3 \right)}}\right) \left(\frac{\log{\left(\left|{\frac{\sqrt{1 - 36 a^{3}}}{2} + \frac{1}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(\sqrt{1 - 36 a^{3}} + 1 \right)}}{\log{\left(3 \right)}}\right) 
=
/                               /|       ___________|\\ /                               /|       ___________|\\
|     /       ___________\      ||      /         3 ||| |     /       ___________\      ||      /         3 |||
|     |      /         3 |      ||1   \/  1 - 36*a  ||| |     |      /         3 |      ||1   \/  1 - 36*a  |||
|I*arg\1 + \/  1 - 36*a  / + log||- + --------------|||*|I*arg\1 - \/  1 - 36*a  / + log||- - --------------|||
\                               \|2         2       |// \                               \|2         2       |//
---------------------------------------------------------------------------------------------------------------
                                                       2                                                       
                                                    log (3)
(log⁡(∣12−1−36a32∣)+iarg⁡(1−1−36a3))(log⁡(∣1−36a32+12∣)+iarg⁡(1−36a3+1))log⁡(3)2\frac{\left(\log{\left(\left|{\frac{1}{2} - \frac{\sqrt{1 - 36 a^{3}}}{2}}\right| \right)} + i \arg{\left(1 - \sqrt{1 - 36 a^{3}} \right)}\right) \left(\log{\left(\left|{\frac{\sqrt{1 - 36 a^{3}}}{2} + \frac{1}{2}}\right| \right)} + i \arg{\left(\sqrt{1 - 36 a^{3}} + 1 \right)}\right)}{\log{\left(3 \right)}^{2}} 
(i*arg(1 + sqrt(1 - 36*a^3)) + log(Abs(1/2 + sqrt(1 - 36*a^3)/2)))*(i*arg(1 - sqrt(1 - 36*a^3)) + log(Abs(1/2 - sqrt(1 - 36*a^3)/2)))/log(3)^2
Respuesta rápida [src] 
        /|       ___________|\                            
        ||      /         3 ||                            
        ||1   \/  1 - 36*a  ||        /       ___________\
     log||- - --------------||        |      /         3 |
        \|2         2       |/   I*arg\1 - \/  1 - 36*a  /
x1 = ------------------------- + -------------------------
               log(3)                      log(3)
x1=log⁡(∣12−1−36a32∣)log⁡(3)+iarg⁡(1−1−36a3)log⁡(3)x_{1} = \frac{\log{\left(\left|{\frac{1}{2} - \frac{\sqrt{1 - 36 a^{3}}}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(1 - \sqrt{1 - 36 a^{3}} \right)}}{\log{\left(3 \right)}} 
        /|       ___________|\                            
        ||      /         3 ||                            
        ||1   \/  1 - 36*a  ||        /       ___________\
     log||- + --------------||        |      /         3 |
        \|2         2       |/   I*arg\1 + \/  1 - 36*a  /
x2 = ------------------------- + -------------------------
               log(3)                      log(3)
x2=log⁡(∣1−36a32+12∣)log⁡(3)+iarg⁡(1−36a3+1)log⁡(3)x_{2} = \frac{\log{\left(\left|{\frac{\sqrt{1 - 36 a^{3}}}{2} + \frac{1}{2}}\right| \right)}}{\log{\left(3 \right)}} + \frac{i \arg{\left(\sqrt{1 - 36 a^{3}} + 1 \right)}}{\log{\left(3 \right)}} 
x2 = log(Abs(sqrt(1 - 36*a^3)/2 + 1/2))/log(3) + i*arg(sqrt(1 - 36*a^3) + 1)/log(3)
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