怎样用对数换底公式得出下列结论?log(a^m)(b^n)=(n/m)logablogab=1/logbalogab*logbc=logac

Question

怎样用 对数 换底公式 得出下列结论?
log(a^m)(b^n) = (n/m)log a b
log a b = 1/log b a
log a b * log b c = log a c

Answer 1

log(a^m)(b^n)=lg(b^n)/lg(a^m)=(nlgb)/(mlga)=(n/m)log a b
log a b=lga/lgb=1/(lgb/lga)=1/log b a
log a b * log b c = (lgb/lga) *(lgc/lgb)=lgc/lga=log a c