求log2(1/125)·log3(1/32)·log5(1/3)
问题描述:
求log2(1/125)·log3(1/32)·log5(1/3)
答
log2(1/125)·log3(1/32)·log5(1/3)=[log2(1)-log2(125)].[log3(1)-log3(32)].[log3(1)-log5(3)]=-log2(5)^3.log5(3).log3(2)^5=-15 log2(5).log3(2).log5(3)=-15 (lg5/lg2).(lg2/lg3).(lg3/lg5)=-15