5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)


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

Penyelesaian:
log 2 4x=1 log 4 x log 2 4x=1 log 2 x log 2 4 log 2 4x=1 log 2 x 2 2 log 2 4x=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=lg1000

Penyelesaian:
2 log x 5+ log 5 x=lg1000 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 x2 )( log 5 x1 )=0 log 5 x=2      or      log 5 x=1 x= 5 2                              x=5 x=25

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