CAT 2018 Question Paper | Quants Slot 1

CAT Questions

This is an Easy-Medium level difficulty question from Logarithms that appeared in CAT 2018 Question Paper. Logarithm is one of the topics where you can score easily and this question is an example of that. Solve these types of questions to master your CAT Preparation Online and the CAT Exam.

Question 27 :If log₂(5 + log₃a) = 3 and log₅(4a + 12 + log₂b) = 3, then a + b is equal to

1. 32
2. 59
3. 67
4. 40

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Logarithms

We know that if log_qp = r then p = q^r
Given log₂(5 + log₃a) = 3
5 + log₃a = 23
log₃a = 3
a = 3³ = 27
Similarly, 4a + 12 + log₂b = 5³
4a + log₂b = 113
log₂b = 5
b = 2⁵ = 32
a + b = 27 + 32 = 59

The question is "If log₂(5 + log₃a) = 3 and log₅(4a + 12 + log₂b) = 3, then a + b is equal to"

Hence, the answer is 59

Choice B is the correct answer.