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

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

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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 logs (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 kx
so that we can get every values in k
We can rewrite this logs (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 logs (pqr) is equal to"

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

Choice C is the correct answer.


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