Question

If $3^{x+y}=81$ and ${81}^{x-y}=3^8$, then find the values ofx and y respectively.

• A. 3, 1
• B. 1, 3
• C. -1, 3
• D. -1, -3

Answer 1

The correct option is A 3, 1

$3^{x+y}=81$
$3^{x+y}=3^4$
$x+y=4$ ---------------- eq 1
${81}^{x-y}=3^8$
$3^{4(x-y)}=3^8$
$4(x-y)=8$
$(x-y)=2$---------------------eq2
Adding eq 1 and 2 we get,
$2x=6$
$x=3$
As $x+y=4$, So $y=1$
Answer (A) 3, 1