[tex] log_{2}(4) + log_{4}(8) + log_{8}(16) + log_{16}(32) [/tex]
[tex] = log_{2}( {2}^{2} ) + log_{ {2}^{2} }( {2}^{3} ) + log_{ {2}^{3} }( {2}^{4} ) + log_{ {2}^{4} }( {2}^{5} ) [/tex]
[tex] = 2 log_{2}(2) + \frac{3}{2} log_{2}(2) + \frac{4}{3} log_{2}(2) + \frac{5}{4} log_{2}(2) [/tex]
[tex] = 2 \times 1 + \frac{3}{2} \times 1 + \frac{4}{3} \times 1 + \frac{5}{4} \times 1[/tex]
[tex] = 2 + \frac{3}{2} + \frac{4}{3} + \frac{5}{4} = \frac{24 + 18 + 16 + 15}{12} = \frac{73}{12} [/tex]
