Question

Срочно, решите пожалуйсто!

Answer 1

1. $log_{26}2+log_{26}13=log_{26}(2*13)=log_{26}26=1$
2. а)  $log_4(2x+10)=log_4(6x-2)$
$2x+10 textgreater 0; 6x-2 textgreater 0$
$x textgreater -5;x textgreater frac{1}{3}$
$2x+10=6x-2$
$4x=12$
$x=3$
б) $log_8(5x-1)=2$
$5x-1 textgreater 0$
$x textgreater frac{1}{5}$
$5x-1=8^2$
$5x=65$
$x=13$
в) $log_5(2x+1)+log_5(16x-7)=3$
$2x+1 textgreater 0;16x-7 textgreater 0$
$x textgreater - frac{1}{2} ;x textgreater frac{7}{16}$
$log_5 ((2x+1)*(16x-7))=log_55^3$
$(2x+1)(16x-7)=125$
$32 x^{2} -14x+16x-7-125=0$
$32 x^{2} +2x-132=0$
$16 x^{2} +x-66=0$
$D=1-4*16*(-66)=1+4224=4225$
$sqrt{D}=65$
$x_1= frac{-1+65}{2*16} = frac{64}{32}=2;x_2= frac{-1-65}{2*16} = frac{-66}{32}=-2 frac{1}{16}$
$x_2$ не входит в ОДЗ.
г) $log_3(5x+1)-log_3(x+1)=1$
$5x+1 textgreater 0;x+1 textgreater 0$
$x textgreater - frac{1}{5} ; x textgreater -1$
$log_3 frac{5x+1}{x+1}=log_33$
$5x+1=3x+3$
$2x=2$
$x=1$