log的一问1/2log2(81)-log2(12)-log2(3)log2是底(log81/log2)=log2(81)

Question

log的一问
1/2log2(81)-log2(12)-log2(3)
log2是底
(log81/log2) = log2(81)

Answer 1

1/2log2(81)-log2(12)-log2(3)
=1/2log2[81/(12*3)]
=1/2log2(9/4)
(log81/log2) = log2(81)
是换底公式
loga（b）=log(c)(b)/log(c)(a)
若有对数loga（b）=x
则a^x=b
a=(x)√b
c^log(c)(a)=(x)√b
c^[x·log(c)(a)]=b
两边取以c为底的对数得x·log(c)(a)=log(c)(b)
x=log(c)(b)/log(c)(a)
即loga（b）=log(c)(b)/log(c)(a)