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CAT 2017 Slot 2 — QA Question 22

LogarithmsEasy

If x is a real number such that log35 = log5(2 + x), then which of the following is true?

Answer & solution

  • A

    0 < x < 3

  • B

    23 < x < 30

  • C

    x > 30

  • 3 < x < 23

Solution

Given log35 = log5(x + 2)

Now log33 < log35 < log39

∴ 1 < log35 < 2
⇒ 1 < log5(x + 2) < 2
⇒ log55 < log5(x + 2) < 2log55
⇒ log55 < log5(x + 2) < log525
⇒ 5 < 2 + x < 25
⇒ 3 < x < 23

Hence, option (d).

CAT 2017 Slot 2 QA Q22: If x is a real number such that log 3 5 = log 5 (2 + x ), then which of the following is true? — Solution | TheCATExam