Quantitative Aptitude – Algebra – Logarithms – If x is a real number

Quantitative Aptitude – Algebra – Logarithms

Question

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

Answer

Option (D)

Solution

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.

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

Logarithm Concepts Questions and Answers for CAT 2018 Quant Preparation

Q1: If log (2^a × 3^b × 5^c) is the arithmetic mean of log (2^2 × 3^3 × 5), log (2^6 × 3 × 5^7), and log(2 × 3^2 × 5^4), then a equals
Check answer of logarithm Q1
Q2: The value of log (base 0.008) √5 + log (base√3) 81 – 7 is equal to Check answer of logarithm Q2 
Q3: Suppose, log(base3)x = log(base12)y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log(base6)G is equal to
Check answer of logarithm Q3

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