# CAT 2017 Question Paper | Quants Slot 2

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

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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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