Finding another solution from the symbolics' hint ?

[lvl107]

Hello Evryone.

From :

Finding another solution from the symbolics' hint ?

Thanks in advance.

[Werner_E]

or even better:

https://www.wolframalpha.com/input/?i=solve+cos(x)%3Dcos(ln(x))

[lvl107]

I greatly appreciate your time and help, Werner. . I got it.

Best Regards.

[lvl107]

Now I have the relative and similar question :

How to make a correction to my guessing-program-function for finding two more solutions in this range ?
Best Regards.

[Fred_Kohlhepp]

As help, the internet, and Werner have shown, the Lambert W function has two branches.  What does Lamb(0,4) give you for zeros?

[lvl107]

Please help and make a correction.

Best Regards.

[Fred_Kohlhepp]

I cannot.  (Only Prime Express--no programming, no symbolics, . . . )

Just type it in your sheet!  Set n := 0

[lvl107]

Many thanks anyway.

Best Regards.

[Werner_E]

Once again you define a function f(x) which describes a whole family of curves, not just one.

The numerics pic a different member of this family when x is negative, but the symbolics only solves one member of the family where you only get real results for x>0.

The get the solutions you are looking for you would have to try to solve a different equation (x -> -x), but you already had a very similar example and have already seen that Mathcad/MuPad is not able to solve symbolically.

So again what remains is to use the numerics.

Can you finally explain and reveal what all those calculations should be good for? If its just playing around it really does not matter if you get symbolic or numeric result, right?

[lvl107]

Werner, I only wish learning and only wish fully understanding the symbolics' hint.(nothing  else). (And because of : "I guess your zeros(  ) program-function already solve it"), (I hope you understand my English as second language), (and again : I only wish learning and only wish fully understanding the symbolics' hint) : 

  

Best Regards.

Loi. 

[Werner_E · Accepted solution]

If you mean understanding the math behind, labert W -function, complex analysis, etc. I think its better to rely on one or more of the many books about this subject rather than watching mathcad struggle with the tasks.

If you mean understanding how to work with Mathcad's symbolics, then you already have learned that Mathcad and especially its symbolics is rather weak when it come to more complex (pun intended) problems and it ever so often fails to provide a solution, provides only part of the solution and in some rare cases even provides a wrong solution.