1. sederhanakan A. 3 log 49 x 7 log 4 x 16 log 9 2.Diket: 2 log 3 = a 3 log 5 = b Tentukan a. 12 log 15 b. 10 log 12

Bab Logaritma

1. 3log 49 × 7log 4 × 16log 9
= 3log (7^2) × 7log 4 × (4^2)log (3^2)
= 2 × 3log 7 × 7log 4 × 2/2 × 4log 3 (sifat (a^m)log (b^n) = n/m × alog b)
= 2 × 3log 4 × 4log 3 (sifat alog b × blog c = alog c)
= 2 × 3log 3
= 2 × 1
= 2

2. 2log 3 = a
2^a = 3

3log 5 = b
3^b = 5

2log 3 × 3log 5 = 2log 5 = ab

a) 12log 15
= 12log (3 × 5)
= 12log 3 + 12log 5
= 1/(3log 12) + 1/(5log 12)
= 1/(3log 3 + 3log 2^2) + 1/(5log 2^2 + 5log 3)
= 1/(1 + 2 × 1/(2log 3)) + 1/(2 × 1/(2log 5) + 1/(3log 5))
= 1/(1 + 2/a) + 1/(2/ab + 1/b)
= 1/(a/a + 2/a) + 1/(2/ab + a/ab)
= 1/((a + 2)/a) + 1/((a + 2)/ab)
= a/(a + 2) + ab/(a + 2)
= a(1 + b)/(a + 2)

b) 10log 12
= 10log (2^2 × 3)
= 10log 2^2 + 10log 3
= 2 × 1/(2log 10) + 1/(3log 10)
= 2/(2log 5 + 2log 2) + 1/(3log 5 + 3log 2)
= 2/(ab + 1) + 1/(b + 1/(2log 3))
= 2/(ab + 1) + 1/(b + 1/a)
= 2/(ab + 1) + 1/(ab/a + 1/a)
= 2/(ab + 1) + 1/((ab + 1)/a)
= 2/(ab + 1) + a/(ab + 1)
= (2 + a)/(ab + 1)