CAT 2020 Question Paper | Quants Slot 1

CAT Questions

Exponents and Logarithms is one of the most commonly tested topics in the CAT exam. Questions from this topic have consistently appeared in every edition of the CAT exam. This question is from Logarithms that tests your understanding of the fundamentals. CAT exam is known to test your basics rather than high funda ideas. With every extra hour you log in for this topic, it becomes exponentially simpler.

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

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Video Explanation

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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})

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

Hence, the answer is, "log₂ (1/3)"