5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)


5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)

Soalan 1:
Selesaikan persamaan, log3 [log2 (2x – 1)] = 2

Penyelesaian:
log3 [log2 (2x – 1)] = 2 ← (jika log a N = x, N = ax)
log2 (2x – 1) = 32
log2 (2x – 1) = 9
2x – 1 = 29
x = 256.5


Soalan 2
Selesaikan persamaan, lo g 16 [ lo g 2 ( 5x 4 ) ]=lo g 9 3  

Penyelesaian:
lo g 16 [ lo g 2 ( 5x 4 ) ]=lo g 9 3 lo g 16 [ lo g 2 ( 5x 4 ) ]= 1 4 log 9 3 = log 9 3 1 2 = 1 2 log 9 3 = 1 2 ( 1 log 3 9 )= 1 2 ( 1 2 )= 1 4 lo g 2 ( 5x 4 )= 16 1 4 lo g 2 ( 5x 4 )=2 5x 4= 2 2 5x=8 x= 8 5

Soalan 3
Selesaikan persamaan, 5 log 4 x =125

Penyelesaian:
5 log 4 x =125 log 5 5 log 4 x = log 5 125 ambil log asas 5 di kedua-dua belah ( log 4 x )( log 5 5 )=3 ( log 4 x )( 1 )=3 x= 4 3 =64


Soalan 4
Selesaikan persamaan, 5 log 5 ( x+1 ) =9

Penyelesaian:
5 log 5 ( x+1 ) =9 log 5 5 log 5 ( x+1 ) = log 5 9 log 5 ( x+1 ). log 5 5= log 5 9 log 5 ( x+1 )= log 5 9 x+1=9 x=8

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