CAT 2020 Slot 1 QA Q21 Logarithms & Exponents

Question 21 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

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

A
log₂(1/3)
B
log₂(1/5)
C
−log₂(1/3)
D
−log₂(1/5)

Answer: (A) log_2(1/3) Logarithms & Exponents MCQ

Solution

Equation: \(2^{y^2\log_3 5} = 5^{\log_2 3}\). Take \(\log_2\): \(y^2\log_3 5 = \log_2 3\cdot\log_2 5\).
\(y^2 = \frac{\log_2 3\cdot\log_2 5}{\log_3 5} = \log_2 3\cdot\log_2 5\cdot\log_5 3 = (\log_2 3)^2\).
y is negative, so \(y = -\log_2 3 = \log_2\frac13\).