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log2/3x-log3x=3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(2)                 
------*x - log(3*x) = 3
  3
xlog⁡(2)3−log⁡(3x)=3x \frac{\log{\left(2 \right)}}{3} - \log{\left(3 x \right)} = 3
Simplificar
Gráfica
05-10-51015202530354045505560-510
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
         /  -3        \
         |-e  *log(2) |
     -3*W|------------|
         \     9      /
x1 = ------------------
           log(2)
x1=−3W(−log⁡(2)9e3)log⁡(2)x_{1} = - \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} 
         /  -3            \
         |-e  *log(2)     |
     -3*W|------------, -1|
         \     9          /
x2 = ----------------------
             log(2)
x2=−3W−1(−log⁡(2)9e3)log⁡(2)x_{2} = - \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} 
x2 = -3*LambertW(-exp(-3)*log(2/9, -1)/log(2))
Suma y producto de raíces [src] 
suma
     /  -3        \      /  -3            \
     |-e  *log(2) |      |-e  *log(2)     |
  3*W|------------|   3*W|------------, -1|
     \     9      /      \     9          /
- ----------------- - ---------------------
        log(2)                log(2)
−3W(−log⁡(2)9e3)log⁡(2)−3W−1(−log⁡(2)9e3)log⁡(2)- \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} - \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} 
=
     /  -3        \      /  -3            \
     |-e  *log(2) |      |-e  *log(2)     |
  3*W|------------|   3*W|------------, -1|
     \     9      /      \     9          /
- ----------------- - ---------------------
        log(2)                log(2)
−3W(−log⁡(2)9e3)log⁡(2)−3W−1(−log⁡(2)9e3)log⁡(2)- \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} - \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} 
producto
    /  -3        \     /  -3            \
    |-e  *log(2) |     |-e  *log(2)     |
-3*W|------------| -3*W|------------, -1|
    \     9      /     \     9          /
------------------*----------------------
      log(2)               log(2)
−3W(−log⁡(2)9e3)log⁡(2)(−3W−1(−log⁡(2)9e3)log⁡(2))- \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} \left(- \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}}\right) 
=
   /  -3        \  /  -3            \
   |-e  *log(2) |  |-e  *log(2)     |
9*W|------------|*W|------------, -1|
   \     9      /  \     9          /
-------------------------------------
                  2                  
               log (2)
9W(−log⁡(2)9e3)W−1(−log⁡(2)9e3)log⁡(2)2\frac{9 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right) W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}^{2}} 
9*LambertW(-exp(-3)*log(2)/9)*LambertW(-exp(-3)*log(2)/9, -1)/log(2)^2
Respuesta numérica [src] 
x1 = 0.0166596927913959
x2 = 32.8530028877753
x2 = 32.8530028877753
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