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x-ln(x+1)=1 equation

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Numerical solution:

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The solution

You have entered [src]
x - log(x + 1) = 1
$$x - \log{\left(x + 1 \right)} = 1$$
The graph
Rapid solution [src]
           /  -2\
x1 = -1 - W\-e  /
$$x_{1} = -1 - W\left(- \frac{1}{e^{2}}\right)$$
           /  -2    \
x2 = -1 - W\-e  , -1/
$$x_{2} = -1 - W_{-1}\left(- \frac{1}{e^{2}}\right)$$
x2 = -1 - LambertW(-exp(-2, -1))
Sum and product of roots [src]
sum
      /  -2\         /  -2    \
-1 - W\-e  / + -1 - W\-e  , -1/
$$\left(-1 - W\left(- \frac{1}{e^{2}}\right)\right) + \left(-1 - W_{-1}\left(- \frac{1}{e^{2}}\right)\right)$$
=
      /  -2\    /  -2    \
-2 - W\-e  / - W\-e  , -1/
$$-2 - W\left(- \frac{1}{e^{2}}\right) - W_{-1}\left(- \frac{1}{e^{2}}\right)$$
product
/      /  -2\\ /      /  -2    \\
\-1 - W\-e  //*\-1 - W\-e  , -1//
$$\left(-1 - W\left(- \frac{1}{e^{2}}\right)\right) \left(-1 - W_{-1}\left(- \frac{1}{e^{2}}\right)\right)$$
=
/     /  -2\\ /     /  -2    \\
\1 + W\-e  //*\1 + W\-e  , -1//
$$\left(W\left(- \frac{1}{e^{2}}\right) + 1\right) \left(W_{-1}\left(- \frac{1}{e^{2}}\right) + 1\right)$$
(1 + LambertW(-exp(-2)))*(1 + LambertW(-exp(-2), -1))
Numerical answer [src]
x1 = -0.841405660436961
x2 = 2.14619322062058
x2 = 2.14619322062058