Question

Calculati: log2 (cos 60°)+log2 (sin 30°) va rog

Answer 1

$=log_{2}~\frac{1}{2}+log_{2}~\frac{1}{2}=$

$=log_{2}(\frac{1}{2}*\frac{1}{2})=$

$=log_{2}(\frac{1}{4})=$

$=log_{2}(\frac{4}{16})$

$=log_{2}4-log_{2}16$

$=log_{2}2^{2}-log_{2}2^{4}$

$=2*log_{2}2-4*log_{2}2$

$=2*1-4*1$

$=2-4=-2$

Answer 2

$\log_{\big2}( \cos60^o) +\log_{\big2}( \sin30^o) = \\ \\ = \log_{\big2} \dfrac{1}{2}+\log_{\big2} \dfrac{1}{2} = \\ \\ = \log_{\big2}2^{-1} +\log_{\big2}2^{-1} = \\ \\ = - \log_{\big2}2 + \Big(-\log_{\big2}2\Big) = \\ \\ = -1 +(-1) = \\ \\ = -1-1 = \\ \\ =-2$