Evaluate 5-3log52 x 22log23

Evaluate 5^-3log₅2 x 2^2log₂3

Correct Answer: Option B

Explanation

5^-3log₅2 x 2^2log₂3i Let -3log₅2 = p => log₅2^-3 = p
∴2^-3 = 5^p
∴5^-3log₅2 = 5log₅2^-3 = 5^pii 2^2log₂3 = q => log₅3² = q
∴3² = 2^q
∴2^22log₂3 = 2^q
= 3² = 9i x ii = 2^-3 x 9 = ¹/_2³ x 9
= ¹/₈ x 9
= ⁹/₈ = 1¹/₈