Hello. Let $C_1,C_2,C_3,q_1,q_2, \epsilon \geq 0 $ and $h \in (0,1)$ it is possible to solve this inequality for $L \in \mathbb{N}$?:
$C_1h^{q_1L}+2C_2C_3h^{q3L}\leq \epsilon$
Ive solved it for some special cases of $q_1$ and $q_2$ and im starting to wonder if its even possible to solve this straight forward.
The inequation can be rewritten
$$ab^L+cd^L\le1$$ with $b,d<1$.
This is a decreasing function of $L$. As $L\in N$, a simple linear search by increasing values of $L$ can do. For better efficiency, you can use an exponential search (doublings) followed by a dichotomic one.