5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)


5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)
Soalan 9
Selesaikan persamaan, log 2 4 x = 1 log 4 x

Penyelesaian:
log 2 4 x = 1 log 4 x log 2 4 x = 1 log 2 x log 2 4 log 2 4 x = 1 log 2 x 2 2 log 2 4 x = 2 log 2 x log 2 16 x 2 = log 2 4 log 2 x log 2 16 x 2 = log 2 4 x 16 x 2 = 4 x x 3 = 4 16 = 1 4 x = ( 1 4 ) 1 3 = 0.62996


Soalan 10
Selesaikan persamaan, log 4 x = 25 log x 4

Penyelesaian:
log 4 x = 25 log x 4 1 log x 4 = 25 log x 4 1 25 = ( log x 4 ) 2 log x 4 = ± 1 5 log x 4 = 1 5 or log x 4 = 1 5 4 = x 1 5 4 = x 1 5 x = 4 5 4 = 1 x 1 5 x = 1024 x 1 5 = 1 4 x = 1 1024


Soalan 11
Selesaikan persamaan, 2 log x 5 + log 5 x = lg 1000

Penyelesaian:
2 log x 5 + log 5 x = lg 1000 2. 1 log 5 x + log 5 x = 3 × ( log 5 x ) 2 + ( log 5 x ) 2 = 3 log 5 x ( log 5 x ) 2 3 log 5 x + 2 = 0 ( log 5 x 2 ) ( log 5 x 1 ) = 0 log 5 x = 2 or log 5 x = 1 x = 5 2 x = 5 x = 25

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