log2( 底数) 1/25*log3(底数)8*log0.2(底数)27

对数换底公式：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(2)1/25×log(3)8×log(0.2)27
=[lg(1/25)/lg2]×(lg8/lg3)×(lg27/lg0.2)
=[(lg1-lg5²)×lg2³×lg3³]/[lg2×lg3×(lg1-lg5)]
=(-2lg5×3lg2×3lg3)/(-lg2×lg3×lg5)
=2×3×3
=18

log(2)1/25×log(3)8×log(0.2)27
=[lg(1/25)/lg2]×(lg8/lg3)×(lg27/lg0.2)
=[(lg1-lg5²)×lg2³×lg3³]/[lg2×lg3×(lg1-lg5)]
=(-2lg5×3lg2×3lg3)/(-lg2×lg3×lg5)
=2×3×3
=18