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CAT Previous Year Paper | CAT Exponents and Logarithms Questions | Question 24

This is a question from Exponents, which tests your understanding of the basics. If you know the concepts of Exponents well, you can exponentially increase your score in this topic. This is a favorite topic of the examiners. Questions from Exponents have appeared more than expected in CAT exam. Make sure you practice this topic well.

Question 24 : If 92x – 1 – 81x-1 = 1944, then x is

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

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Explanatory Answer

Method of solving this CAT Question from Exponents and Logarithms

We have to find the value of x
⟹ 92x – 1 – 81x-1 = 1944
⟹ 92x – 1 – (92)x-1 = 1944
⟹ 92x – 1 – 92x - 2 = 1944
⟹ (92x - 2 × 9) - 92x - 2 = 1944
⟹ 92x - 2 × (9 - 1) = 1944
⟹ 92x - 2 = \\frac{1944}{8}) = 243
We can write 243 = 35 = 9\\frac{5}{2})
Comparing the powers,
⟹ 2x – 2 = \\frac{5}{2})
⟹ 2x = \\frac{9}{2})
⟹ x = \\frac{9}{4})

The question is "If 92x – 1 – 81x-1 = 1944, then x is"

Hence, the answer is \\frac{9}{4})

Choice B is the correct answer

 

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