Question

If ${\log }_{2}x+{\log }_{2}y\ge 6,$then the least value of x+y is

• A. 4
• B. 8
• C. 16
• D. 32

Answer 1

Answer: (C)

16

${\log }_{2}x+{\log }_{2}y\ge 6$
$\Rightarrow xy\ge 64$ ...(1)
If $x>0$ & $y>0$
Since $A.M.\ge G.M$
$\Rightarrow \frac{x+y}{2}\ge \sqrt{xy}$
$\Rightarrow \frac{x+y}{2}\ge \sqrt{64}$ ....{ From 1}
$\Rightarrow x+y\ge 16$
Ans: C