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

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

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

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

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

Can we create any inequalities from the information we’re given in the question?

Is it helpful to note that \(\log_{2}x\) is an increasing function?