Solving an equation with nested ceilings How would I go about solving something like the following for $x$ in terms of $y$?
$$1+\left \lceil \log_{x-1} \left ( \left \lceil \frac{y}{x} \right \rceil \right ) \right \rceil = 2$$
I've never had to solve an equation with a ceiling before, never mind nested ceilings. Even Wolfram Alpha Pro is timing out to the point of not being able to go anywhere.

$$1+\left \lceil \log_{x-1} \left ( \left \lceil \frac{y}{x} \right \rceil \right ) \right \rceil = 2$$
$$\left \lceil \log_{x-1} \left ( \left \lceil \frac{y}{x} \right \rceil \right ) \right \rceil = 1$$
$$0 \lt \log_{x-1} \left ( \left \lceil \frac{y}{x} \right \rceil \right )  \le 1$$
assuming $x \gt 2$:
$$1 \lt  \left \lceil \frac{y}{x} \right \rceil \le x-1$$ 
$$1 \lt   \frac{y}{x} \le \lfloor x-1 \rfloor$$
$$x \lt  y \le x \lfloor x-1 \rfloor.$$
Note if $1 \lt x \lt 2$ then you need to solve $x-1 \le  \left \lceil \frac{y}{x} \right \rceil \lt 1$, which would require you to find an integer between $0$ and $1$. You may have problems with the logarithm base $x-1$ if $x=2$ or $x \le 1$. 
