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3+2*log(x+1)*3=2*log3*(x+1) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
3 + 2*log(x + 1)*3 = 2*log(3)*(x + 1)
$$3 \cdot 2 \log{\left(x + 1 \right)} + 3 = \left(x + 1\right) 2 \log{\left(3 \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
        /  -1/2        \           /  -1/2            \
        |-e    *log(3) |           |-e    *log(3)     |
     3*W|--------------|        3*W|--------------, -1|
        \      3       /           \      3           /
-1 - ------------------- + -1 - -----------------------
            log(3)                       log(3)        
$$\left(-1 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right) + \left(-1 - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right)$$
=
        /  -1/2        \      /  -1/2            \
        |-e    *log(3) |      |-e    *log(3)     |
     3*W|--------------|   3*W|--------------, -1|
        \      3       /      \      3           /
-2 - ------------------- - -----------------------
            log(3)                  log(3)        
$$-2 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}} - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}$$
producto
/        /  -1/2        \\ /        /  -1/2            \\
|        |-e    *log(3) || |        |-e    *log(3)     ||
|     3*W|--------------|| |     3*W|--------------, -1||
|        \      3       /| |        \      3           /|
|-1 - -------------------|*|-1 - -----------------------|
\            log(3)      / \              log(3)        /
$$\left(-1 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right) \left(-1 - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right)$$
=
/   /  -1/2        \         \ /   /  -1/2            \         \
|   |-e    *log(3) |         | |   |-e    *log(3)     |         |
|3*W|--------------| + log(3)|*|3*W|--------------, -1| + log(3)|
\   \      3       /         / \   \      3           /         /
-----------------------------------------------------------------
                                2                                
                             log (3)                             
$$\frac{\left(3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right) + \log{\left(3 \right)}\right) \left(3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right) + \log{\left(3 \right)}\right)}{\log{\left(3 \right)}^{2}}$$
(3*LambertW(-exp(-1/2)*log(3)/3) + log(3))*(3*LambertW(-exp(-1/2)*log(3)/3, -1) + log(3))/log(3)^2
Respuesta rápida [src]
             /  -1/2        \
             |-e    *log(3) |
          3*W|--------------|
             \      3       /
x1 = -1 - -------------------
                 log(3)      
$$x_{1} = -1 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}$$
             /  -1/2            \
             |-e    *log(3)     |
          3*W|--------------, -1|
             \      3           /
x2 = -1 - -----------------------
                   log(3)        
$$x_{2} = -1 - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}$$
x2 = -1 - 3*LambertW(-exp(-1/2)*log(3/3, -1)/log(3))
Respuesta numérica [src]
x1 = 5.45976753447716
x2 = -0.18147669861784
x2 = -0.18147669861784