运用对数换底公式化简log2(3)*log3(4)*log4(5)*log5(2),

log2(3)*log3(4)*log4(5)*log5(2)=log2(3)*log3(2^2)*log2^2(5)*log5(2)=log2(3)*2log3(2)*1/2 * log2(5)*log5(2) (2与1/2约分了)=log2(3)*1/log2(3) * log2(5) * 1/log2(5)=1