# 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 $$[0,1)$$.

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