Sederhanakanlah. e. 4 lo g 9 ⋅ 3 lo g 125 ⋅ 25 lo g 16

Pembahasan

Ingat sifat-sifat logaritma dan eksponen berikut: a m lo g b n ​ = ​ m n ​ ⋅ a lo g b ​ a lo g a ​ = ​ 1 ​ a lo g b ⋅ b lo g c = a lo g c Jika basis tidak ditulis, maka nilainya adalah 10. Berdasarkan sifat tersebut, maka 4 lo g 9 ⋅ 3 lo g 125 ⋅ 25 lo g 16 ​ = = = = = = ​ 2 2 lo g 3 2 ⋅ 3 lo g 5 3 ⋅ 5 2 lo g 2 4 2 2 ​ ⋅ 2 lo g 3 ⋅ 3 3 ​ ⋅ 3 lo g 5 ⋅ 2 4 ​ ⋅ 5 lo g 2 1 ⋅ 1 ⋅ 2 ⋅ 2 lo g 3 ⋅ 3 lo g 5 ⋅ 5 lo g 2 2 ⋅ 2 lo g 2 2 ⋅ 1 2 ​ Jadi, diperoleh nilai 4 lo g 9 ⋅ 3 lo g 125 ⋅ 25 lo g 16 ​ = ​ 2 ​ .