Question

Выполните задания .......

Answer 1

Решение задания приложено

Answer 2

$1)3^{x}*2^{1-x}=5*2^{x}*3^{1-x} \\\\3^{x}*2*2^{-x}=5*2^{x}*3*3^{-x}\\\\2*(\frac{3}{2})^{x}=15*(\frac{2}{3} )^{x}\\\\2*(\frac{3}{2})^{2x}=15\\\\(\frac{3}{2})^{2x}=15\\\\2x=log_{1,5}15\\\\x=log_{1,5}\sqrt{15}$

$2)2^{log_{3}5 }=5^{log_{3}2 }\\\\5^{log_{3}2 } -0,1<5^{log_{3} 2}\\\\2^{log_{3}5 }-0,1<5^{log_{3}2 }$

$3)\frac{log_{2}70 }{log_{280} 2}-\frac{log_{2}560 }{log_{35}2 }=log_{2}70*log_{2}280-log_{2}560*log_{2}35=log_{2} (35*2)*log_{2}(35*8)-log_{2}(35*16)*log_{2}35=(log_{2}35+log_{2}2)(log_{2}35+log_{2}8)-(log_{2}35+log_{2}16)*log_{2}35=(log_{2}35+1)(log_{2}35+3)-(log_{2} 35+4)*log_{2}35=$$log_{2} ^{2}35+3log_{2}35+log_{2}35+3-log_{2} ^{2}35-4log_{2}35=3$