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Question 25 : If 9^{x - (\\frac{1}{2}))} – 2^{2x – 2} = 4^x – 3^{2x – 3}, then x is

1. \\frac{3}{2})
2. \\frac{2}{5})
3. \\frac{3}{4})
4. \\frac{4}{9})

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Exponents and Logarithms

Given that 9^{x - (\\frac{1}{2}))} – 2^{2x – 2} = 4^x – 3^{2x – 3}
⟹ \\frac{9^x}{9^{\frac{1}{2}}}) - \\frac{2^{2x}}{2^2}) = 2^2x - \\frac{3^{2x}}{3^3})
⟹ \\frac{3^{2x}}{3}) - \\frac{2^{2x}}{4}) = 2^2x - \\frac{3^{2x}}{27})
⟹ \\frac{(9 × 3^{2x}) + 3^{2x}}{27}) = \\frac{(4 × 2^{2x}) + 2^{2x}}{4})
⟹ 3^2x × \\frac{10}{27}) = 5 × \\frac{2^{2x}}{4})
⟹ 3^2x × 8 = 2^2x × 27
⟹ 3^{2x - 3} = 2^{2x - 3}
⟹ 2x - 3 = 0
⟹ x = \\frac{3}{2})

The question is "If 9^{x - (\\frac{1}{2}))} – 2^{2x – 2} = 4^x – 3^{2x – 3}, then x is"

Hence, the answer is \\frac{3}{2})

Choice A is the correct answer