3.设3x=4y=36,求+的值.
解 由已知分别求出x和y,
∵3x=36,4y=36,∴x=log336,y=log436,
由换底公式得:
x==,y==,
∴=log363,=log364,
∴+=2log363+log364=log36(32×4)=log3636=1.
4.计算:
(1)log89×log2732;
(2)log927;
(3)log2×log3×log5;
(4)(log43+log83)(log32+log92).
解 (1)log89×log2732=×
=×=×=;
(2)log927====;
(3)log2×log3×log5
=log25-3×log32-5×log53-1
=-3log25×(-5log32)×(-log53)