5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)
Soalan 12
Selesaikan persamaan,
Penyelesaian:
Soalan 13
Diberi bahawa 2 log2 (x – y) = 3 + log2 x + log2y. Buktikan x2 + y2– 10xy = 0.
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
x2
– 2xy + y2 = 8xy
x2 + y2 – 10xy = 0 (terbukti)Soalan 14
Diberi bahawa 2 log2 (x + y) = 3 + log2 x + log2y. Buktikan x2 + y2= 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
x2
+ 2xy + y2 = 8xy
x2 + y2 = 6xy (terbukti)