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 16x=6  

Penyelesaian:
log 2 5 x + log 4 16x=6 log 2 5 x + log 2 16x log 2 4 =6 log 2 5 x + log 2 16x 2 =6 2 log 2 5 x + log 2 16x=12 log 2 ( 5 x ) 2 + log 2 16x=12 log 2 ( 25x )+ log 2 16x=12 log 2 ( 25x )( 16x )=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 + log2 y. Buktikan x2 + y2 – 10xy = 0.

Penyelesaian:
2 log2 (xy) = 3 + log2 x + log2 y
log2 (xy)2 = log2 8 + log2 x + log2 y
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 + log2 y. Buktikan x2 + y2 = 6xy.

Penyelesaian:
2 log2 (x + y) = 3 + log2 x + log2 y
log2 (x + y)2 = log2 8 + log2 x + log2 y
log2 (x + y)2 = log2 8xy
(x + y)2 = 8xy
x2 + 2xy + y2 = 8xy
x2 + y2 = 6xy  (terbukti)

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