How to solve an equation with an array of constant parameters?

I am trying to solve equation xlogx=e where x is the variable and e is a real constant. e can take many (say 10000) values which are stored in an array e_arr. I want to return an array of numerical solutions with each element corresponding to an element of e_arr. Of course, I can construct a string 'x*log2(x)= - 0.1' for example for each of the element of e_arr, but is there any way to call solve (or vpasolve) function with vector input for the constant parameter e? Could you please help me with this, assuming you are given an array, say, e_arr=[-0.1, -0.54, -0.32, ... ..., -0.79, -0.6]? Thanks a lot. PS: the log function has base 2 and x takes values in [0.0, 1.0].

Answer 1

[Ridwan Alam]

syms x e
>> eqns = x*log2(x)==e
 
eqns =
 
(x*log(x))/log(2) == e
 
>> S= solve(eqns,x)
 
S =
 
(e*log(2))/lambertw(0, e*log(2))
 
>> e=[-0.1, -0.54, -0.32, -0.79, -0.6];
 
>> subs(S)
 
ans =
 
[ -log(2)/(10*lambertw(0, -log(2)/10)), -(27*log(2))/(50*lambertw(0, -(27*log(2))/50)), -(8*log(2))/(25*lambertw(0, -(8*log(2))/25)), -(79*log(2))/(100*lambertw(0, -(79*log(2))/100)), -(3*log(2))/(5*lambertw(0, -(3*log(2))/5))] 

[Heng Zhou]

My question is not about an array of variables, but and array of constants.

[Ridwan Alam]

The answer is updated. Hope this helps.

[Heng Zhou]

Thanks. So the handling of array of constants is not in solve(), but in symbolic functions (subs). Anyway, it is a way out. Thank you for your prompt answer (PS, fsolve is also a good idea).

[Ridwan Alam]

Sure. Glad to help. Please vote up if you liked the conversation.