CAT 2017 Question Paper | Quants Slot 2

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Are you planning to start your CAT Preparation Online for this year? CAT previous year paper will lead you in the right direction. They help you understand the level of difficulty that the cputs you through. Start preparaing with this Logarithms question from CAT 2017 Question Paper Slot 2.
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Question 22 : If x is a real number such that log₃5 = log₅(2 + x), then which of the following is true ?

1. 0 < x < 3
2. 23 < x < 30
3. x > 30
4. 3 < x < 23

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Exponents and Logarithms

log₃ 5 = log₅ (2 + x)
Since log₃ 3 = 1 and log₃ 9 = 2 , we can say that 2 > log₃ 5 > 1
We need to find the range of x
If log₅ (2 + x) > 1
⟹ 2 + x > 5
⟹ x > 3
If log₅ (2 + x) < 2
⟹ 2 + x < 5²
⟹ 2 + x < 25
⟹ x < 23
Therefore 3 < x < 23

The question is "If x is a real number such that log₃5 = log₅(2 + x), then which of the following is true ?"

Hence, the answer is 3 < x < 23

Choice D is the correct answer

 

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