Log^2 3(x-1) - 2 log(1/3)[9/(x-1)] = 2^[log 2(7)] решите пожалуйста

Question

Log^2 3(x-1) - 2 log(1/3)[9/(x-1)] = 2^[log 2(7)] решите пожалуйста

Answer 1

log²(3)(x-1)-2log(-3)(9/(x-1)=7                 ODЗ x-1>0   x>1

log²(3)(x-1)+2(log(3)(9)-log(3)(x-1))=7

log²(3)(x-1)+2(2-log(3)(x-1))=7

log²(3)(x-1)+4-2log(3)(x-1)-7=0

log²(3)(x-1)-2log(3)(x-1)-3=0

log(3)(x-1)=t

t²-2t-3=0     D=4+12=16

t1=(2+4)/2=3    t2=(2-4)/2=-1    log(3)(x-1)=3            log(3)(x-1)=-1

                      x-1=3³   x-1=27    x=28                        x-1=1/3    x=4/3