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Verified answer
LogAritMa[(½)'log 3 + (¼)'log 9] [³log ¼ + 9'log ½]
= (½)'log (3 × 9^½) × ³log (¼ . (½)^½)
= (½)'log 3² × ³log (½)^(5/2)
= 2 × 5/2
= 5 ✔