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e^z1*e^z2=e^z1+z2

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e^z1*e^z2=e^z1+z2 equation

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Numerical solution:

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The solution

You have entered [src]
 z1  z2    z1     
e  *e   = e   + z2
$$e^{z_{1}} e^{z_{2}} = z_{2} + e^{z_{1}}$$
The graph
Sum and product of roots [src]
sum
   /        z1\      
   |  z1 - e  |    z1
- W\-e        / - e  
$$\left(- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)\right)$$
=
   /        z1\      
   |  z1 - e  |    z1
- W\-e        / - e  
$$- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)$$
product
   /        z1\      
   |  z1 - e  |    z1
- W\-e        / - e  
$$\left(- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)\right)$$
=
   /        z1\      
   |  z1 - e  |    z1
- W\-e        / - e  
$$- e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)$$
Rapid solution [src]
          /        z1\      
          |  z1 - e  |    z1
z2_1 = - W\-e        / - e  
$$z_{2 1} = - e^{z_{1}} - W\left(- e^{z_{1} - e^{z_{1}}}\right)$$