Zadanie Oblicz (funkcja log) a) log_{ \frac{1}{4} } \frac{2 \sqrt[5]{64} }{ \sqrt{8}}
b) log_{ \frac{1}{2}} 4+log_{ \frac{1}{3}}6-log_{ \frac{1}{3}}8
źródło:
a) log_{ \frac{1}{4} } \frac{2 \sqrt[5]{64} }{ \sqrt{8}}=log_{\frac{1}{4}}\frac{2*64^{\frac{1}{5}}}{8^{\frac{1}{2}}}=log_{\frac{1}{4}}\frac{2*(2^6)^{\frac{1}{5}}}{(2^3)^{\frac{1}{2}}}=log_{\frac{1}{4}}\frac{2*2^{\frac{6}{5}}}{2^{\frac{3}{2}}}=log_{\frac{1}{4}}\frac{2^{\frac{5+6}{5}}}{2^{\frac{3}{2}}}=log_{\frac{1}{4}}\frac{2^{\frac{11}{5}}}{2^{\frac{3}{2}}}=log_{\frac{1}{4}}2^{\frac{22}{10}-\frac{15}{10}}=log_{\frac{1}{4}}2^{\frac{7}{10}}=log_{\frac{1}{4}}(\sqrt4)^{\frac{7}{10}}=log_{\frac{1}{4}}(4^{\frac{1}{2}})^{\frac{7}{10}}=log_{\frac{1}{4}}4^{\frac{7}{20}}=log_{\frac{1}{4}}(\frac{1}{4})^{-\frac{7}{20}}=-\frac{7}{20}