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Given log₅(N) = I1 + f1 and log₃(N) = I2 + f2, where I1 and I2 are integers and f1, f2 are in [0, 1). If I1 = 2 and I2 = 3, what is the maximum integer value of N?

1. 79
2. 80
3. 81
4. 82

Correct answer: 80

Solution

From I1=2: 25 <= N < 125. From I2=3: 27 <= N < 81. Intersection: 27 <= N < 81. The maximum integer value is 80.

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