Question

Помогите пожалуйста!35 баллов​

Answer 1

$17)\frac{log_{3}14 }{log_{9}14}=\frac{log_{3}14 }{log_{3}14^{\frac{1}{2}}}=\frac{log_{3}14 }{\frac{1}{2}log_{3}14}=2\\\\18)\frac{log_{6}81 }{log_{6}9}=\frac{log_{6}9^{2}}{log_{6}9}=\frac{2log_{6}9}{log_{6}9}=2$

$19)5^{log_{25}49}=5^{log_{5}7}=7\\\\20)log_{\sqrt{8}}^{2}64=log_{8}^{2}(8^{2})^{2}=log_{8}^{2}8^{4}=16log_{8}^{2}8=16\\\\21)9^{3log_{9} 11} =(9^{log_{9}11})^{3}=11^{3} =1331$

$22)4^{log_{2}\sqrt{3}}=4^{log_{4}3}=3\\\\23)log_{4}log9_{81}=log_{4}2=\frac{1}{2}\\\\24)\frac{60}{4^{log_{4} 10}}=\frac{60}{10}=6\\\\25)log_{\frac{1}{8}}\sqrt{8}=log_{8^{-1}}8^{\frac{1}{2}}=log_{8} 8^{-\frac{1}{2}} =-\frac{1}{2}log_{8}8=-\frac{1}{2}$

$26)\frac{4^{log_{6} 72} }{4^{log_{6}2}}=\frac{4^{log_{6}36}*4^{log_{6}2}}{4^{log_{6}2}} =4^{2}=16\\\\27)\frac{log_{3}\sqrt{5}}{log_{3}5}=\frac{log_{3}5^{\frac{1}{2}}}{log_{3}5}=\frac{\frac{1}{2}log_{3}5}{log_{3}5}=\frac{1}{2}$

$28)(5^{log_{3}7})^{log_{7} 3}=5^{log_{3}7*log_{7}3}=5^{1}=5$