Question

设a,b均大于1,且loga(c)logb(c)=4,则下列不等式中一定成立的是 ( )

Answer 1

loga(c)logb(c)=4 ,即 logc(a)logc(b)=1/4 (此处用了换底公式）.

而 logc(a) + logc(b) >= 2根号【logc(a)logc(b)】= 2根号【1/4】= 1

即 logc(ab) >= 1 = logc(c) 即 ab >= c ,故B