If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true?

A) 0 < x < 3

B) 23 < x < 30

C) x > 30

D) 3 < x < 23

Option (D)

From CAT 2017 – Quantitative Aptitude – Algebra – Logarithms, we can see that,

Log(base 3)5 lies between 1 and 2 because Log(base 3)3 = 1 and Log(base 3)9 = 2

1 < Log(base 3)5 < 2

So, log(base 5)(2+x) should also lie between 1 and 2

1 < log(base 5)(2+x) < 2

5^1 < 2+x < 5^2

5 < 2+x < 25

3 < x < 23

Option D is the right answer.

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