Question

va rog rapid!
log in baza 2 din 4+log in baza 4 din 8+log in baza 8 din 16+log in baza 16 din 32!

Answer 1

$log_{2}(4) + log_{4}(8) + log_{8}(16) + log_{16}(32)$

$= log_{2}( {2}^{2} ) + log_{ {2}^{2} }( {2}^{3} ) + log_{ {2}^{3} }( {2}^{4} ) + log_{ {2}^{4} }( {2}^{5} )$

$= 2 log_{2}(2) + \frac{3}{2} log_{2}(2) + \frac{4}{3} log_{2}(2) + \frac{5}{4} log_{2}(2)$

$= 2 \times 1 + \frac{3}{2} \times 1 + \frac{4}{3} \times 1 + \frac{5}{4} \times 1$

$= 2 + \frac{3}{2} + \frac{4}{3} + \frac{5}{4} = \frac{24 + 18 + 16 + 15}{12} = \frac{73}{12}$