CAT 2017 Question Paper | Quants Slot 1

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 9^{2x – 1} – 81^x-1 = 1944, then x is

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

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Exponents and Logarithms

We have to find the value of x
⟹ 9^{2x – 1} – 81^x-1 = 1944
⟹ 9^{2x – 1} – (9²)^x-1 = 1944
⟹ 9^{2x – 1} – 9^{2x - 2} = 1944
⟹ (9^{2x - 2} × 9) - 9^{2x - 2} = 1944
⟹ 9^{2x - 2} × (9 - 1) = 1944
⟹ 9^{2x - 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 9^{2x – 1} – 81^x-1 = 1944, then x is"

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

Choice B is the correct answer

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