Question

`x=log_5 3+log_7 5+log_9 7`
A. `ain[3//2,oo)`
B. `ain[(1)/(2^(1//3),oo)`
C. `ain[(3)/(2^(1//3),oo)`
D. none of these.

Answer 1

Correct Answer - C
Using `A.M.geG.M.,` we have
`(a)/(3)=(log_(5)3+log_(7)5+log_(9)7)/(3)ge(log_(5)3xxlog_(7)5xxlog_(9)7)^(1//3)`
`impliesage3(log_(9)3)^(1//3)impliesage3((1)/(2))^(1//3)impliesain[(3)/(2^(1//3)),oo)`