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 p^{3} = q^{4} = r^{5} = s^{6}, then the value of log_{s} (pqr) is equal to

- \\frac{24}{5})
- 1
- \\frac{47}{10})
- \\frac{16}{5})

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Given that p^{3} = q^{4} = r^{5} = s^{6}

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 p^{3} = q^{4} = r^{5} = s^{6} 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 p^{3} = q^{4} = r^{5} = s^{6} = k^{60}

Or p = k^{20} q = k^{15} r = k^{12} s = k^{10}

\\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 p ^{3} = q^{4} = r^{5} = s^{6}, then the value of log_{s} (pqr) is equal to"**

Choice C is the correct answer.

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