Question

设a>1,函数f(x)=log(a)x在区间[a,2a]上的最大值与最小值之差为1/2,则a=

详细过程

Answer 1

因为log(a)x在a>1时递增,所以在a时取最小,在2a时取最大.所以差为log(a)2a-log(a)a=log(a)2=1/2
所以a=4

Answer 2

log(a) 2a - log(a) a =1/2
log(a) 2a=3/2
log(a)2 =1/2
a^(1/2)=2
a=4