4. Logaritma.Mr.Sukani

Logaritma

Logaritma

Konsep dasar

ax _{= y ↔} a_{log y = x ; dimana a > 0 ; y > 0 dan a ≠1}

catatan : 10_{log x cukup ditulis dengan log x . Contoh: 2}3 _{= 8 ↔} 2_{log 8 = 3}

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Sifat – sifat logaritma

1. a_{log a = 1 contoh :} 4_{log 4 = 1}

2. a_{log a}n _{= n contoh :} 2_{log 8 =} 2_{log 2}3 _{= 3} 2_{log 2 = 3}

3. a_{log 1 = 0 contoh :} 5_{log 1 =} 5_{log 5}0 _{= 0}

4. log an _{= n log a contoh : log 9 = log 3}2 _{= 2 . log 3}

5.a_{log = - n contoh :} 2_{log =} 2_{log =} 2_{log 2}-3 _{= -3}

6. -n contoh : 1/2_{log 4 =} 1/2_{log = -2}

7. a_{log b = contoh : =} 3_{log 27 =} 3_{log 3}3 _{= 3}

8.g_{log a +} g_{log b =} g_{log a x b contoh :} 6_{log 12 +} 6_{log 3 =} 6_{log 36 =} 6_{log 6}2 _{= 2}

9. contoh : 3_{log 54 –} 3_{log 2 =} 3_{log =} 3_{log 27 = 3}

10. a_{log b .} b_{log c .} c_{log d =} a_{log d contoh :} 2_{log 5 .}5_{log 3 .} 3_{log 8 =} 2_{log 8 = 3}

11. = . a_{log b contoh :} 27_{log 25 = = .} 3_{log 5}

a log n

a 1



a log

b log

d c log d

log - c

log g g

g



2 54

m n

a _logb

n m

2 3 3 _log5

Contoh:

1. Nilai dari 2_{log 16 +} 3_{log 81 –} 4_{log 64 –} 5_{log 1 adalah :}

Jawab : = 2_{log 16 +} 3_{log 81 –} 4_{log 64 –} 5_{log 1}

= 2_{log 2}4 ₊ 3_{log 3}4 _– 4_{log 4}3 _– 5_{log 5}0

= 4 + 4 – 3 – 0 = 5

2. Nilai dari 3_{log 18 +} 3_{log 15 –} 3_{log 10 = ….}

Jawab : = 3_{log 18 +} 3_{log 15 –} 3_{log 10}

=

= 3_{log 27}

= 3_{log 3}3

= 3

3. Jika a = log 3 dan b = log 5, tentukan nilai 9_{log 25.}

Jawab :

9_{log 25 = = = = =}

4. Jika log 3 = x dan log 5 = y. Hitung nilai dari : log 0,15 Jawab :

log 0,15 = log

= log 3 + log 5 – log 100 = x + y - 2

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10 15 . 18 log 3

9 log

25 log

2 2

3 log

5 log

3 log 2

5 log 2

a b

2 2

a b