If log (2^a Ã— 3^b Ã— 5^c) is the arithmetic mean of log (2^2 Ã— 3^3 Ã— 5), log (2^6 Ã— 3 Ã— 5^7), and log(2 Ã— 3^2 Ã— 5^4), then a equals

3

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

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