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Question 21 : If y is a negative number such that 2y2log35 = 5log23, then y equals

  1. log(1/3)
  2. log(1/5)
  3. −log(1/3)
  4. −log(1/5)

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Explanatory Answer

Taking log on both sides
y2log35 log 2 = log23 log 5
Choosing the base to be 3
y2 log35 log32 = log23 log35
y2 log32 = log23 (Cancelling log35)
y2 = log23/log32
y2 = (log23)2
y = - log23 (Given y is a negative number)
y = log2\\frac{1}{3})

The question is "If y is a negative number such that 2y2log35 = 5log23, then y equals"

Hence, the answer is, "log(1/3)"

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