Question

Срочно!1-3-4 задания

Answer 1

$1.;log_27-log_263+2log_26=log_27-log_263+log_236=log_2left(frac{7cdot36}{63}right)=\=log_24=log_22^2=2\\3.a);5^x-7cdot5^{x-2}=90\5^x-7cdot5^xcdot5^{-2}=90\5^x-frac7{25}cdot5^x=90\frac{18}{25}cdot5^x=90\5^x=90:frac{18}{25}\5^x=90cdotfrac{25}{18}\5^x=5cdot25\5^x=125\5^x=5^3\x=3$

$b);log_frac12(x^2-4x-1)=-2\O.D.3.:\x^2-4x-1 textgreater 0\(x-2-sqrt5)(x-2+sqrt5) textgreater 0\xin(-infty;2-sqrt5)cup(2+sqrt5;;+infty)\\log_{2^{-1}}(x^2-4x-1)=-2\-log_2(x^2-4x-1)=-2\log_2(x^2-4x-1)=2\x^2-4x-1=4\x^2-4x-5=0\D=16 +20=36\x_{1,2}=frac{4pm6}2\x_1=-1\x_2=5$

$4.;a);9^{0,5x^2-3} textless 27\3^{2(0,5x^2-3)} textless 3^3\x^2-6 textless 3\x^2 textless 9\-3 textless x textless 3\xin(-3;;3)\\b);log_frac17(3-x) textgreater -1\log_{7^{-1}}(3-x) textgreater -1\-log_7(3-x) textgreater -1\log_7(3-x) textless 1\3-x textless 7\x textgreater -4$