CAT 2018 Question Paper | Quants Slot 2

CAT Questions

The CAT Previous Year Paper consist of a vareity of questions from Logarithms.. The test takers generally get frightened by taking a look at the questions with "logs." Only way to ace these questions is with regular practice. Here is a question that requires you to use basic Logarithm laws. Try solving this question on your own.
To pratice more previously asked CAT questions, visit CAT Previous Year Papers.

Question 9 : If p³ = q⁴ = r⁵ = s⁶, then the value of log_s (pqr) is equal to

1. \\frac{24}{5})
2. 1
3. \\frac{47}{10})
4. \\frac{16}{5})

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Logarithm

Given that p³ = q⁴ = r⁵ = s⁶
We have to find the value of log_s (pqr)
Since more variables are given, to avoid confusion assume a new variable to simplify it.
Let us assume this p³ = q⁴ = r⁵ = s⁶ is equal to k^x
so that we can get every values in k
We can rewrite this log_s (pqr) as \\frac{log_k (pqr)}{log_k s})
Now let us take the LCM of 3 , 4 , 5 and 6 which is equal to 60
Hence p³ = q⁴ = r⁵ = s⁶ = k⁶⁰
Or p = k²⁰ q = k¹⁵ r = k¹² s = k¹⁰
\\frac{log_k (pqr)}{log_k s}) = \\frac{log_k k^{20}k^{15}k^{12}}{log_k k^{10}})
\\frac{log_k (pqr)}{log_k s}) = \\frac{47}{10})

The question is "If p³ = q⁴ = r⁵ = s⁶, then the value of log_s (pqr) is equal to"

Hence, the answer is \\frac{47}{10})

Choice C is the correct answer.