log1/2(9^(x-1)-5)=log1/2(3(x-1)-2)-2

log1/2[9^(x-1)-5]=log1/2[3^(x-1)-2]-2
log1/2[9^(x-1)-5]=log1/2[3^(x-1)-2]-log1/2(1/2)^2
log1/2[9^(x-1)-5]=log1/2{[3^(x-1)-2]÷(1/4)}
log1/2[9^(x-1)-5]=log1/2{4[3^(x-1)-2]}
9^(x-1)-5=4*3^(x-1)-8
令a=3^(x-1)
则9^(x-1)=a²
所以a²-4a+3=0
a=1,a=3
3^(x-1)=1,则真数3^(x-1)-2