log2(3)*log3(4)*log4(5)*....log(k+1)(k+2)=log2(k+2) 怎么证
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利用换底公式:log（a）（b）=log(n)(b)/log(n)（a）:
log2(3)*log3(4)*log4(5)*....log(k+1)(k+2)
=log2(3)*[log2(4)/log2(3)]*[log2(5)/log2(4)]*...*[log2(k+1)/log2(k)]*[log2(k+2)/log2(k+1)]
=log2(k+2)
log2(3)*log3(4)*log4(5)*....log(k+1)(k+2)
=log2(3)*[log2(4)/log2(3)]*[log2(5)/log2(4)]*...*[log2(k+1)/log2(k)]*[log2(k+2)/log2(k+1)]
=log2(k+2)
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