Diketahui bahwa 3 lo g x ⋅ 6 lo g x ⋅ 9 lo g x = 3 lo g x ⋅ 6 lo g x + 3 lo g x ⋅ 9 lo g x + 6 lo g x ⋅ 9 lo g x Tentukan nilai x (ada dua jawaban)

Pembahasan

Ingat a m lo g b = m 1 ​ ⋅ a lo g b a lo g b = c lo g a c lo g b ​ a lo g b = b lo g a 1 ​ a lo g f ( x ) = b ⇒ f ( c ) = a c Perhatikan perhitungan berikut 3 lo g x ⋅ 6 lo g x ⋅ 9 lo g x = 3 lo g x ⋅ 6 lo g x + 3 lo g x ⋅ 9 lo g x + 6 lo g x ⋅ 9 lo g x 3 lo g x ⋅ 6 lo g x ⋅ 3 2 lo g x = 3 lo g x ⋅ 6 lo g x + 3 lo g x ⋅ 3 2 lo g x + 6 lo g x ⋅ 3 2 lo g x 2 1 ​ ⋅ 3 lo g x ⋅ 6 lo g x ⋅ 3 lo g x = 3 lo g x ⋅ 6 lo g x + 2 1 ​ ⋅ 3 lo g x ⋅ 3 lo g x + 2 1 ​ ⋅ 6 lo g x ⋅ 3 lo g x 2 1 ​ ⋅ ( 3 lo g x ) 2 ⋅ 6 lo g x = 3 lo g x ⋅ 6 lo g x + 2 1 ​ ⋅ ( 3 lo g x ) 2 + 2 1 ​ ⋅ 6 lo g x ⋅ 3 lo g x 2 1 ​ ⋅ 3 ( lo g x ) 2 ⋅ 6 lo g x − 2 1 ​ ⋅ ( 3 lo g x ) 2 = 3 lo g x ⋅ 6 lo g x + 2 1 ​ ⋅ 6 lo g x ⋅ 3 lo g x 2 1 ​ ⋅ 3 ( lo g x ) 2 ⋅ 6 lo g x − 2 1 ​ ⋅ ( 3 lo g x ) 2 = 2 3 ​ ⋅ 3 lo g x ⋅ 6 lo g x 2 1 ​ ⋅ 3 ( lo g x ) 2 ⋅ 3 l o g 6 3 l o g x ​ − 2 1 ​ ⋅ ( 3 lo g x ) 2 = 2 3 ​ ⋅ 3 lo g x ⋅ 3 l o g 6 3 l o g x ​ 3 ( lo g x ) 2 ⋅ 3 l o g 6 3 l o g x ​ − ( 3 lo g x ) 2 = 3 ⋅ 3 lo g x ⋅ 3 l o g 6 3 l o g x ​ 3 l o g 6 1 ​ ⋅ ( 3 lo g x ) 3 − ( 3 lo g x ) 2 = 3 l o g 6 3 ​ ⋅ ( 3 lo g x ) 2 3 l o g 6 1 ​ ⋅ ( 3 lo g x ) 3 − ( 3 lo g x ) 2 − 3 l o g 6 3 ​ ⋅ ( 3 lo g x ) 2 = 0 ( 3 lo g x ) 2 ( 3 l o g 6 3 l o g x ​ − 1 − 3 l o g 6 3 ​ ) = 0 ( 3 lo g x ) 2 ( 6 lo g 3 ⋅ 3 lo g x − 1 − 3 ⋅ 6 lo g 3 ⋅ ) = 0 ​ Dari persamaan tersebut, diperoleh ( 3 lo g x ) 2 3 lo g x = 0 x x ​ = = = ​ 0 3 0 1 ​ atau 6 lo g 3 ⋅ 3 lo g x − 1 − 3 ⋅ 6 lo g 3 6 lo g 3 ⋅ 3 lo g x = 1 + 3 ⋅ 6 lo g 3 3 lo g x = 6 l o g 3 6 l o g 6 + 6 l o g 3 3 ​ 3 lo g x = 6 l o g 3 6 l o g 162 ​ 3 lo g x = 3 lo g 162 x ​ = = ​ 0 162 ​ Dengan demikian, nilai x yang memenuhi persamaan di tersebut adalah x = 0 atau x = 162 .