Question

If $8^x2^y=512$ and $3^{3x+2y}=(3^2)^{(3\times2)}$ then what is the value of x and y ?

• A. (1,3)
• B. (2, 3)
• C. (2, 4)
• D. (1,4)

Answer 1

Answer: (B)

(2, 3)

Answer 2

$\text{Given: } 8^{3x} 2^y = 512 \\\\$
$\Rightarrow 2^{3x} \times 2^y = (2^9) \\\\$
$\Rightarrow 2^{3x + y} = (2)^9 \\\\$
$\Rightarrow 3x + y = 9 \quad \text{-------- (i)} \\\\$
$\text{Also, } 3^{3x + 2y} = (3^2)(3^2) \\\\$
$\Rightarrow 3^{3x + 2y} = (3)^{12} \\\\$
$\Rightarrow 3x + 2y = 12 \quad \text{-------- (ii)} \\\\$
$\text{Solving equations (i) and (ii), we get: } x = 2 \text{ and } y = 3 \\\\$
The correct answer is (B) : (2,3)