Question : If $2^{2x-y}=16$ and $2^{x+y}=32$, the value of $xy$ is:
Option 1: $2$
Option 2: $4$
Option 3: $6$
Option 4: $8$
Answer (1)
18th Jan, 2024
Correct Answer: $6$
Solution :
Given: $2^{2x-y}=16$
$⇒2^{2x-y}=2^4$
$⇒2x-y=4$--------------------(1)
Again, $2^{x+y}=32$
$⇒2^{x+y}=2^5$
$⇒x+y=5$ ---------------------(2)
Solving equations (1) and (2), we get:
$x=3$ and $y= 2$
$\therefore xy=3×2=6$
Hence, the correct answer is $6$.
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