已知log8^9=a,log2^5=b,则lg3=?

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已知log8^9=a,log2^5=b,则lg3=?

已知log8^9=a,log2^5=b,则lg3=?
已知log8^9=a,log2^5=b,则lg3=?

已知log8^9=a,log2^5=b,则lg3=?
先介绍换底公式:log(a)b=lgb/lga
证明:设log(a)b=t
则a^t=b,两边取以10为底的对数
lga^t=lgb
tlga=lgb
所以t=lgb/lga
所以log(a)b=lgb/lga
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log(8)9=a ==> lg9/lg8=a ==> 2lg3/(3lg2)=a ==> lg3=(3a/2)lg2
log(2)5=b ==> lg5/lg2=b ==> (lg10-lg2)/lg2=b ==> lg2=1/(b+1)
由此可得,lg3=3a/[2(b+1)]