# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Exponents and Logarithms Questions | Question 22

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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##### 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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