Question

С подробным решением, пожалуйста

Answer 1

ОДЗ x>0 U 9-x>0⇒x<9
x∈(0;9)
log(7)(9-x)-log(21)(9-x)=log(7)(9-x)- lof(7)(9-x)/(1+log(7)3)=
=log(7)(9-x)(1+log(7)3-1)/(1+log(7)3)=log(7)(9-x)*log(7)3/(1+log(7)3)

log(21)x-log(63)x=log(7)x/(1+log(7)3) -log(7)x/(1+2log(7)3)=
=log(7)x(1+2log(7)3-1-log(7)3)/(1+log(7)3)(1+2log(7)3)=
log(7)x*log(7)3/(1+log(7)3)(1+2log(7)3)

[log(7)(9-x)-log(21)(9-x)]/[log(21)x-log(63)x]=
=log(7)(9-x)*log(7)3/(1+log(7)3) :log(7)x*log(7)3/(1+log(7)3)(1+2log(7)3)=
=log(7)(9-x)*log(7)3/(1+log(7)3) * (1+log(7)3)(1+2log(7)3)/l og(7)x*log(7)3=
=log(7)(9-x)*(1+2log(7)3)/log(7)x

log(7)(9-x)*(1+2log(7)3)/log(7)x≤1+2log(7)3
log(7)(9-x)/log(7)x≤1
log(7)(9-x)≤log(7)x
9-x≤x
2x≥9
x≥4,5
Ответ x∈[4,5;9)