if log2 x+ log2 y >= 6 then the least va...

if `log_2 x+ log_2 y >= 6` then the least value of `x+y`

A

4

B

8

C

16

D

32

Text Solution

Verified by Experts

The correct Answer is:

C

Given ` log_(2) x + log_(2) y ge 6`
` rArr log_(2) (xy) ge 6`
` rArr xy ge 64`
Also to define ` log_(2) x and log_(2) y `, we have
` x gt 0, y gt 0`.
Since A.M.` ge G.M., `we have
` (x+y)/2 ge sqrt(xy)`
` or x + y ge 2 sqrt(xy) ge 16`

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