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CAT 2018 Slot 1 — QA Question 24

LogarithmsEasy

If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is equal to

Answer & solution

  • A

    40

  • B

    67

  • 59

  • D

    32

Solution

log2(5 + log3a) = 3
⇒ (5 + log3a) = 23 = 8
⇒ log3a = 3
⇒ a = 33 = 27

log5(4a + 12 + log2b) = 3
⇒ log5(4 × 27 + 12 + log2b) = 3
⇒ 120 + log2b = 53
⇒ log2b = 125 - 120
⇒ log2b = 5
⇒ b = 25 = 32

∴ a + b = 27 + 32 = 59

Hence, option (c).

CAT 2018 Slot 1 QA Q24: If log 2 (5 + log 3 a) = 3 and log 5 (4a + 12 + log 2 b) = 3, then a + b is equal to — Solution | TheCATExam