Question

Log_2(x-1)^2 - log_0,5(x-1)=9

Answer 1

Log2(x-1)^2=2log2(x-1)=2log0,5(x-1)/log0.5(2)
тогда 2log0,5(x-1)/log0.5(2) - log0.5(x-1)=9
(2log0.5(x-1)-log0.5(2)*log0.5(x-1))/log0.5(2)=9
log0.5(x-1)(2-log0.5(2))/log0.5(2)=9
log0.5(x-1)(log0.5(0.5^3))/log0.5(2)=9
3log0.5(x-1)/log0.5(2)=9
3log2(x-1)=9
log2(x-1)=3
log2(x-1)=log2(8)
x-1=8
x=9
ответ:9