Logarithms

Algebra Level 4

A cool number is defined as a number $N$ that satisfies both of the following equations simultaneously. $\log_3 N = 4 + \beta_1 \\ \log_5 N = 2 + \beta_2$ $\beta_1$ and $\beta_2$ are fractional parts of the number. How many integral cool numbers are there?

Note: A fractional part lies in the interval $[0,1)$ .