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

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