Jika 5^log 3 =a dan 3^log 4 =b, tentukan : 12^log 75 ,Dan 3^log 40

jawab

⁵log 3 .³log 4 = a b
⁵log 4 = ab

¹²log 75 = ⁵log 75 / ⁵log 12
= (⁵log 5². 3) / (⁵log 4. 3)
= (2 + ⁵log 3) / (.⁵log 4 + ⁵log 3)
= (2 + a )/ ( ab + a)

³log 40 = (⁵log 40)/ (⁵log 3)
= (⁵log 5 + ⁵log 2 + ⁵log 4) / (⁵log 3)
= ( 1 + 1/2 ab + ab) /(a)
= ( 1+ 3/2 ab) /(a)
= 1/2 (2 + 3ab)/(a)
= (2 + 3ab)/(2a)