5.5.2 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)


5.5.2 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)
Soalan 5:
Selesaikan persamaan, log 9 ( x 2 ) = log 3 2

Penyelesaian:
log 9 ( x 2 ) = log 3 2 log a b = log c b log c a log 3 ( x 2 ) log 3 9 = log 3 2 log 3 ( x 2 ) 2 = log 3 2 log 3 ( x 2 ) = 2 log 3 2 log 3 ( x 2 ) = log 3 2 2 x 2 = 4 x = 6


Soalan 6:
Selesaikan persamaan, log 9 ( 2 x + 12 ) = log 3 ( x + 2 )

Penyelesaian:
log 9 ( 2 x + 12 ) = log 3 ( x + 2 ) log 3 ( 2 x + 12 ) log 3 9 = log 3 ( x + 2 ) log 3 ( 2 x + 12 ) = 2 log 3 ( x + 2 ) log 3 ( 2 x + 12 ) = log 3 ( x + 2 ) 2 2 x + 12 = x 2 + 4 x + 4 x 2 + 2 x 8 = 0 ( x + 4 ) ( x 2 ) = 0 x = 4 (tidak diterima) x = 2


Soalan 7:
Selesaikan persamaan, log 4 x = 3 2 log 2 3

Penyelesaian:
log 4 x = 3 2 log 2 3 log 2 x log 2 4 = 3 2 log 2 3 log 2 x 2 = 3 2 log 2 3 log 2 x = 2 × 3 2 log 2 3 log 2 x = 3 log 2 3 log 2 x = log 2 3 3 x = 27


Soalan 8:
Selesaikan persamaan, 2 log 5 2 = log 2 ( 2 x )

Penyelesaian:
2 log 5 2 = log 2 ( 2 x ) 2 = log 5 2. log 2 ( 2 x ) 2 = 1 log 2 5 . log 2 ( 2 x ) 2 log 2 5 = log 2 ( 2 x ) log 2 5 2 = log 2 ( 2 x ) 25 = 2 x x = 23

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