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: $8$
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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