log2(3)*log3(4)*log4(5)*.log(k+1)(k+2)=log2(k+2) 怎么证

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log2(3)*log3(4)*log4(5)*.log(k+1)(k+2)=log2(k+2) 怎么证
log2(3)*log3(4)*log4(5)*.log(k+1)(k+2)=log2(k+2) 怎么证

log2(3)*log3(4)*log4(5)*.log(k+1)(k+2)=log2(k+2) 怎么证
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)