Can we find bounds for $\log_2 3$?

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Observe that \(2^3 = 8\), \(2^5 = 32\), \(3^2 = 9\) and \(3^3 = 27\). From these facts, we can deduce that \(\log_{2}3\), the logarithm of \(3\) to base \(2\), is

1. between \(1\frac{1}{3}\) and \(1\frac{1}{2}\);

2. between \(1\frac{1}{2}\) and \(1\frac{2}{3}\);

3. between \(1\frac{2}{3}\) and \(2\);

4. between \(2\) and \(3\).