Question

Сделайте !!!! Срочноооо !!!!!

Answer 1

А) log(3)x=2log(9)6-log(9)12<=>log(3)x=log(9)36-log(9)12<=>log(3)x=log(9)(36:12)<=>log(3)x=log(9)3<=>log(3)x=log(3^2)3<=>log(3)x=1/2<=>3^1/2=x; x=sqrt{3}
Ответ: sqrt{3}.
Б) log(1/2)x=log(0,2)35-2log(0,2)25*sqrt{7}=log(0,2)35-log(0,2)25*7=log(0,2)(35/175)=log(0,2)0,2<=>log1/2x=1; 1/2^1=x, x=1/2.
Ответ: 1/2.
В) log(5)x=1/2log(3)144+log(3)0,75=log(3)12+log(3)0,75=log(3)(12*0,75)=log(3)9<=>log(5)x=log(3)9<=>log(5)x=log(3)3^2<=>log(5)x=2; 5^2=x; x=25.
Ответ: 25.
Г) log(pi)x=3log(0,1)4+2log(0,1)1,1/4;
log(pi)x=log(0,1)64+log(0,1)(5/4)^2;
log(pi)x=log(0,1)(64*25/16);
log(pi)x=log(0,1)100;
log(pi)x=log(10^-1)10^2;
log(pi)x=-2log(10)10;
log(pi)x=-2<=>pi^-2=x <=>x=pi^-2=1/pi^2.
То есть log(pi)1/pi^2=log(pi)pi^-2; -2log(pi)pi=-2.
Ответ: 1/pi^2 (pi^-2).