Note that we know $\log_c y$ is an integer, so $\log_c 2$ must also be an integer, hence $c^k=2$ for some $k\in\mathbb{Z}$.  If we also assume $c$ is an integer, then the problem does in fact have a unique solution.  Hope this helps.

Homework with logarithms
This question may be way too specific, but what is the word for someone who surveys land in search for Oil (for petroleum). I think it might be a scientific word, like one that ends with -ist (like biologist)
