5.6 Indeks dan Logaritma, SPM Praktis (Soalan Panjang)


5.6 Indeks dan Logaritma, SPM Praktis (Soalan Panjang)
Soalan 3:
Diberi bahawa p = 3r dan q = 3t, ungkapkan yang berikut dalam sebutan r dan/ atau t.
(a)  log 3 p q 2 27 ,  
(b)  log9 p – log27 q.

Penyelesaian:
(a)
Diberi p = 3r, log3 p = r
q = 3t, log3 q = t

log 3 p q 2 27
= log3 pq2 – log3 27
= log3 p + log3 q2 – log3 33
= r + 2 log3 q – 3 log3 3
= r + 2 log3 q – 3(1)
= r + 2t – 3

(b)
log9 p – log27 q
= log 3 p log 3 9 log 3 q log 3 27 = r log 3 3 2 t log 3 3 3 = r 2 log 3 3 t 3 log 3 3 = r 2 t 3   



Soalan 4:
(a)  Permudahkan:
log2 (2x + 1) – 5 log4 x2 + 4 log2 x
(b)  Seterusnya, selesaikan persamaan:
log2 (2x + 1) – 5 log4 x2 + 4 log2 x = 4

Penyelesaian:
(a)
log2 (2x + 1) – 5 log4 x2 + 4 log2 x
= log 2 ( 2x+1 ) 5 log 2 x 2 log 2 4 +4 log 2 x = log 2 ( 2x+1 ) 5 2 log 2 x 2 + log 2 x 4 = log 2 ( 2x+1 ) log 2 ( x 2 ) ( 5 2 ) + log 2 x 4  
= log 2 ( 2x+1 ) log 2 x 5 + log 2 x 4 = log 2 ( 2x+1 )( x 4 ) x 5 = log 2 2x+1 x  

(b)
log2 (2x + 1) – 5 log4 x2 + 4 log2 x = 4
log 2 2x+1 x =4        2x+1 x = 2 4        2x+1 x =16       2x+1=16x          14x=1             x= 1 14


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