ABC26GN1884 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
If $8^{x}.2^{y}=512$ and $3^{3x+2y}=9^{6}$, then what is the value of $x$ and $y$ ? (M.A.T., 2004)
Answer
Explanation
$$8^{x}2^{y}=512 \Leftrightarrow \left(2^{3}\right)^{x}.2^{y}=2^{9} \Leftrightarrow 2^{3x+y}=2^{9} \Leftrightarrow 3x+y=9$$ And, $$3^{3x+2y}=9^{6} \Leftrightarrow 3^{3x+2y}=\left(3^{2}\right)^{6}=3^{12} \Leftrightarrow 3x+2y=12$$ Subtracting (i) from (ii): $y=3$. Putting $y=3$ in (i): $3x=6$, so $x=2$. Hence, $x=2$ and $y=3$.
Explanation as extracted from the printed page; notation may be imperfect.
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