Evaluate 5-3log52 x 22log23

Explanation

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

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