ABC26GN1990 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
What are the values of $x$ and $y$ that satisfy the equation $2^{0.7 x} \cdot 3^{-1.25 y}=\frac{8 \sqrt{6}}{27}$ ? (C.A.T., 2006)
(a)x = 2.5, y = 6
(b)x = 3, y = 5
(c)x = 3, y = 4
(d)x = 5, y = 2
Answer
Explanation
$2^{0.7 x} \cdot 3^{-1.25 y}=\frac{8 \sqrt{6}}{27} \Leftrightarrow \frac{2^{0.7 x}}{3^{1.25 y}}=\frac{2^{3} \cdot 2^{\frac{1}{2}} \cdot 3^{\frac{1}{2}}}{3^{3}}=\frac{2^{\left(3+\frac{1}{2}\right)}}{3^{\left(3-\frac{1}{2}\right)}}=\frac{2^{\frac{7}{2}}}{3^{\frac{5}{2}}}=\frac{2^{3.5}}{3^{2.5}}. \therefore 0.7 x=3.5 \Rightarrow x=\frac{3.5}{0.7}=5$ and $1.25 y=2.5 \Rightarrow y=\frac{2.5}{1.25}=2$.
Explanation as extracted from the printed page; notation may be imperfect.
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