Question

求几道对数化简题的答案

利用对数的换底公式化简 1.loga(c)3*logc(a) 2.log2(3)*log3(4)*log4(5)*log5(2) 3.(log4(3)+log8(3))*(log3(2)+log9(2)) 请把过程写出来，谢谢!

Answer 1

1.
lgc/lga×lga/lgc
=1
2.log2(3)*log3(4)*log4(5)*log5(2)
=lg2/lg3×lg3/lg4×lg4/lg5×lg5/lg2
约分
=1/lg2×lg2
=1
3.(log4(3)+log8(3))*(log3(2)+log9(2))
=(log2底^2对3+log2底^3对3）×（log3底2+log3底^2对2）
次数移到前面来
=（1/2log2底3+1/3log2底3）×（log3底2+1/2log3底2）
同底对数之和相乘
之差相除
=5/6log2底9×1/2log3底4
=5/6log2底3^2×log3底2^2
=5/3log2底3×log3底2
=5/3(lg3/lg2×lg2/lg3)
=5/3