If \( 2^{x} \times 3^{y} = 12 \) and \( 2^{y} \times 3^{x} = 18 \), then the value of x + y is :
3
Multiply the two equations: \( 2^{x} \times 3^{y} \times 2^{y} \times 3^{x} = 12 \times 18 \).
\( 2^{x + y} \times 3^{x + y} = 216 \Rightarrow 6^{x + y} = 6^{3} \).
Comparing powers of the same base, x + y = 3.
Check: \( 12 = 2^{2} \times 3^{1} \) gives x = 2, y = 1, and then \( 2^{1} \times 3^{2} = 18 \) holds, so x + y = 2 + 1 = 3.
Hence, 3.
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