# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Logarithms Questions | Question 27

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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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##### Method of solving this CAT Question from Logarithms

We know that if logqp = r then p = qr
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.

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