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

The Correct Option is B

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