Question

if `log_2 x+ log_2 y >= 6` then the least value of `x+y`
A. 4
B. 8
C. 16
D. 32

Answer 1

Correct Answer - 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`