Б
ОДЗ
x-5>0⇒x>5
log(2)4/(x-5)=log(2)4-log(2)(x-5)=2-log(2)(x-5)=2+log(0,5)(x-5)
(3/5)^[log(3/5)1/4+log(3/5)8]=(3/5)^log(3/5)2=2
получим уравнение
log²(0,5)(x-5)+2+log(0,5)(x-5)=2
log²(0,5)(x-5)+log(0,5)(x-5)=0
log(0,5)(x-5)*(log(0,5)(x-5)+1)=0
[log(0,5)(x-5)=0⇒x-5=1⇒x=6
[log(0,5)(x-5)+1=0⇒log(0,5)(x-5)=-1⇒x-5=2⇒x=7
Ответ x=6;x=7
в
ОДЗ x>0
прологарифмируем обе части
(lgx+11)/6*lgx=(lgx+1)*lg10
(lgx+11)/6*lgx-(lgx+1)=0
(lgx+11)*lgx-6(lgx+1)=0
lgx=a
(a+11)*a-6(a+1)=0
a²+11a-6a-6=0
a²+5a-6=0
a1+a2=-5 U a1*a2=-6
a1=-6⇒lgx=-6⇒x=0,000001
a2=1⇒lgx=1⇒x=10