5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)


5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)
Soalan 12
Selesaikan persamaan, log 2 5 x + log 4 16 x = 6

Penyelesaian:
log 2 5 x + log 4 16 x = 6 log 2 5 x + log 2 16 x log 2 4 = 6 log 2 5 x + log 2 16 x 2 = 6 2 log 2 5 x + log 2 16 x = 12 log 2 ( 5 x ) 2 + log 2 16 x = 12 log 2 ( 25 x ) + log 2 16 x = 12 log 2 ( 25 x ) ( 16 x ) = 12 log 2 400 x 2 = 12 400 x 2 = 2 12 x 2 = 10.24 x = 3.2


Soalan 13
Diberi bahawa 2 log2 (xy) = 3 + log2 x + log2y. Buktikan x2 + y– 10xy = 0.

Penyelesaian:
2 log2 (xy) = 3 + log2x + log2 y
log2 (xy)2 = log2 8 + log2 x + log2y
log2 (xy)2 = log2 8xy
(xy)2 = 8xy
x2– 2xy + y2 = 8xy
x2 + y2 – 10xy = 0 (terbukti)


Soalan 14
Diberi bahawa 2 log2 (x + y) = 3 + log2 x + log2y. Buktikan x2 + y= 6xy.
 
Penyelesaian:
2 log2 (x + y) = 3 + log2x + log2 y
log2 (x+ y)2 = log2 8 + log2 x + log2y
log2 (x+ y)2 = log2 8xy
(x + y)2 = 8xy
x+ 2xy + y2 = 8xy
x2 + y2 = 6xy  (terbukti)

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