CAT 2018 Slot 1 — QA Question 22

Given, 2^x = $3^{{\log }_5\left(2\right)}$

⇒ 2^x = $2^{{\log }_5\left(3\right)}$

⇒ x = log₅3

Option (a): 1 + ${\log }_3\left(\frac{5}{3}\right)$ = 1 + log₃5 - log₃3 = log₃5

Option (b): log₅9 = 2(log₅3)

Option (c): log₅8 = 3(log₅2)

Option (d): 1 + ${\log }_5\left(\frac{3}{5}\right)$ = 1 + log₅3 - log₅5 = log₅3

Hence, option (d).