∵(√1oga^b-2)+|loga^c-3|=0
∴ 1oga^b-2=0 |loga^c-3|=0
∴1oga^b=2 loga^c=3
∴ lgb/lga=2 lgb=2lga
lgc/lga=3 lgc=3lga
log b^c=lgc/lgb=3lga/2lga=3/2