Quantitative Aptitude – Algebra – Logarithms – If log (2^a × 3^b × 5^c)

Quantitative Aptitude – Algebra – Logarithms

Question

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

Answer

3

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Logarithms, we can see that,
log (2^a. 3^b. 5^c) = [log (2^2.3^3.5) + log (2^6.3.5^7) + log (2.3^2.5^4)]/3
3 * log (2^a. 3^b. 5^c) = log (2^9.3^6.5^12)
log (2^a. 3^b. 5^c)^3 = log (2^9.3^6.5^12)
log (2^3a. 3^3b. 5^3c) = log (2^9.3^6.5^12)
3a = 9
a=3
Answer: 3

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

Logarithm Concepts Questions and Answers for CAT 2018 Quant Preparation

Q1: If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true?
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

Other posts related to Quantitative Aptitude – Algebra

Problems on Ages with complete solutions, answers, and tricks to solve
How to Solve Number of Integral Solutions Questions for CAT 2017
Quadratic Equations
Basic Functions and Modifications of Graphs
An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam​​