number of integer solutions for $2^x\cdot 3^y$ Can someone help me figure out how to calculate the number of integer solutions to the equation: $N\ge2^x3^y|x,y\in\Bbb Z+$ 
For example if $N$ is $30$ we have $2\cdot 3$, $2^2\cdot 3$, $2^3\cdot 3$, $2\cdot 3^2$ so $4$ solutions
I know the number of integer solutions to $N\ge2^x$ is just $\left \lfloor \ln{N}/\ln{2} \right \rfloor $
So I was thinking something along the lines of taking the sum of $\log_2\left(\frac{N}{3^i}\right)$ from $i=1..(\log_3(N))$
Any help is greatly appreciated


The problem $2^x 3^y \le 30$ can be solved graphically as follows.
Taking the logarithm of both sides and simplifying, we get
\begin{align}
   2^x 3^y &\le 30 \\
   (\ln 2)x + (\ln 3)y &\le \ln 30 \\
\end{align}
The line above is the line described by $(\ln 2)x + (\ln 3)y = \ln 30$.
The indicated lattice points are the $(x,y)$ solutions to $ 2^x 3^y \le 30$
