**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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