Question

Помогите, лагорифмы!!!

Answer 1

$161)log_{36}216=log_{36}(36*6)=log_{36}36+log_{36}6=1+log_{6}6^{\frac{1}{2} }=1+\frac{1}{2}log_{6}6=1+0,5=1,5\\\\162)log_{11}77-log_{11} 7=log_{11}\frac{77}{7}=log_{11}11=1$

$163)log_{20}0,05+log_{0,02}2500=log_{20}\frac{1}{20}+log_{\frac{1}{50} }50^{2}=log_{20}20^{-1}+log_{50}50^{-2}=-1-2=-3$

$164)log_{0,7}100-log_{0,7}49=log_{0,7}\frac{100}{49}=log_{0,7}(0,7)^{-2}=-2$

$165)\frac{log_{17}8 }{log_{17}2 }=\frac{log_{17}2^{3}}{log_{17}2 }=\frac{3log_{17}2}{log_{17}2 }=3$

$166)\frac{log_{5}93 }{log_{25}93 }=\frac{log_{5}93 }{log_{5}93^{\frac{1}{2}}}=\frac{log_{5} 93}{\frac{1}{2}log_{5}93}=\frac{1}{\frac{1}{2}} =2$