Consider $$a~q^x~+~b~y^x~+~c~z^x~= \text{constant}~.$$ Now, I have the values of $~q,~ y ,~$ and $~z~$ as well as the constant.
I need to solve the equation to obtain $~a,~ b ~$ and $~c~$ and the powers of $~q,~ y ,~$ and $~z~$ such that it satisfies the equation.
Thank you.
You have to many variables and to little equations to find a unique solution. In this circumstance I would suggest taking $x=0$. I will assume without loss of generality that $q\neq0$ so we can take $a=\text{constant}$ and $b=c=0$.