Trzeba obliczyć: a) log64 log16 log4 16 b) log0,4(2+log0,25(1-log4 2)) c) log2 pierwiastek z 120 +log2 pierwiastek z 30 - log2 15

a) korzystam ze wzoru log_a a^b=b log_{64} log_{16} log_4 16= log_{64} log_{16} log_4 4^2= log_{64}log_{16} 2= =log_{64} log_{16} 16^{\frac{1}{4}}=log_{64} \frac{1}{4}=x 64^x=\frac{1}{4} 4^{3x}=4^{-1} 3x=-1 x=\frac{-1}{3} zatem log_{64} log_{16} log_4 16=\frac{-1}{3} b) log_{0,4}(2+log_{0,25}(1-log_4 4^{\frac{1}{2}}))= =log_{0,4}(2+log_{0,25}(1-\frac{1}{2}))= =log_{0,4}(2+log_{\frac{1}{4}}\frac{1}{2})= =log_{0,4}(2+log_{\frac{1}{4}}(\frac{1}{4})^{\frac{1}{2}}= =log_{0,4}(2+\frac{1}{2})= =log_{\frac{4}{10}} 2\frac{1}{2}= =log_{\frac{2}{5}} \frac{5}{2}= =log_{\frac{2}{5}} (\frac{2}{5})^{-1}=-1 c) =log_2(\sqrt{120}*\sqrt{30})-log_2 15= log_2 \sqrt{3600} - log_2 15= =log_2 60 - log_2 15=log_2(60:15)=log_2 4=log_2 2^2=2