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(log2 6)×(log3 6)%(log2 3+log3 2)=

对 log(a) (M·N)=log(a) M+log(a) N

设所有等式的值为t 所以a=2^(t-2) b=3^(t-3) a+b=6^t 所以1/a+1/b=(a+b)/ab=6^t/[2^(t-2)*3^(t-3)]=6^t/[(2^t)/4*(3^t)/27]=108

log2 6*log3 6-(log2 3 +log3 2) =log2 6*log3 6-log2 3-log3 2 =log2(3x2)*log3 (3x2)-log2 3-log3 2 =(log2 3+log2 2)(log3 3+log3 2)-log2 3-log 3 2 =(log2 3+1)(log3 2+1)-log2 3-log 3 2 =log23*log32+log3 2+log 23+1-log2 3-log 32 =log...

loga(b)*logb(c)=loga(c); loga(b)*logb(c)*logc(d)=loga(d). log2(3)*log3(4)*log4(5)*log5(6)*log6(7)*log7(8)=log2(8)=3,所以3=loga(b),所以b=a^3

log4(15)+log5(4) =log4(3)+log4(5)+log5(4) ≥log4(3)+2√[log4(5)*log5(4)] =log4(3)+2, log2(3)+log3(8)+log4(3) =3/2log2(3)+3log3(2) ≥2√[3/2log2(3)*3log3(20)] =3√2, ∴原式≥3√2+2>6。

换底公式:loga b=(logc b)/(logc a) 所以log2 36=(log6 36)/(log6 2) log3 36=(log6 36)/(log6 3)

log2(108)

∵方程x+log2x=6的根为α,方程x+log3x=6的根为β,∴log2x=6-x,log3x=6-x,log2α=6-α,log3β=6-β,令f(x)=log2x,g(x)=log3x,h(x)=6-x,画出图形:∴α<β,故选C.

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