5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)


5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)
Soalan 5:
Selesaikan persamaan, log 9 ( x2 )= log 3 2  

Penyelesaian:
log 9 ( x2 )= log 3 2 log a b= log c b log c a log 3 ( x2 ) log 3 9 = log 3 2 log 3 ( x2 ) 2 = log 3 2 log 3 ( x2 )=2 log 3 2 log 3 ( x2 )= log 3 2 2 x2=4 x=6


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

Penyelesaian:
log 9 ( 2x+12 )= log 3 ( x+2 ) log 3 ( 2x+12 ) log 3 9 = log 3 ( x+2 ) log 3 ( 2x+12 )=2 log 3 ( x+2 ) log 3 ( 2x+12 )= log 3 ( x+2 ) 2 2x+12= x 2 +4x+4 x 2 +2x8=0 ( x+4 )( x2 )=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 ( 2x )

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

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