Jika x dan y memenuhi persamaan (2²logx ²logy 3²logy ²logx) (1 4) = (5 5),
maka x . y = ....
Jawab:
(2²logx ²logy)( 1 ) ₌ ( 5 )
(3²logy ²logx)( 4) ( 5 )
Misal
²logx = a
²logy = b
(2a b)( 1 ) ₌ ( 5 )
(3b a)( 4 ) ( 5 )
2a + 4b = 5
3b + 4a = 5
2a + 4b = 5 | × 2 | 4a + 8b = 10
4a + 3b = 5 | × 1 | 4a + 3b = 5 _
5b = 5
b = 1
²log y = 1
y = 2
y = 2
2a + 4b = 5
2a + 4(1) = 5
2a = 5 – 4
2a = 1
a = ½
2log x = ½
x = 2½
x = √2
Jadi x . y = √2 × 2
= 2√2