rumus dan contoh soal logaritma

RUMUS LOGARITMA DAN CONTOH SOAL

 Bentuk alog a = 1
Contoh :
2log 2 = 2log 21 = 1
log 10 = log 101 = 1

 Bentuk alog 1 = 0
Contoh :
2
log 1 = 2log 20 = 0
4

log 1 = 4log 40 = 0

 Bentuk alog b = 1/ blog a
Contoh :
2
log 8 = 1 / (8log 2) = 1 / (8log 81/3) = 1/ (1/3) = 3
64

log 4 = 1 / (4log 64) = 1 / (4log 43) = 1/3

 Bentuk alog b = nlog b / nlog a [Syarat n > 0 dan n ≠ 1]
Contoh :
2
log 16 = (4log 16) / (4log 2) = (4log 42) / (4log 41/2) = 2/ (1/2) = 4
4

log 64 = (2log 64) / (2log 4) = (2log 26) / (2log 22) = 6/2 = 3

 Bentuk aalog b = b
Contoh :
1616log 32 = 32

42log 4 = 22(2log 4) = 2(2log 4 + 2log 4) = 2(2log 4). 2(2log 4) = 4.4 = 16

 Bentuk alog (b.c) = alog b + alog c
Contoh :
2
log (16.2) = 2log 16 + 2log 2 = 4 + 1 = 5

4

log (32.2) = 4log 32 + 4log 2 = 4log 16 + 4log 2 + 4log 2 = 4log 16 +4log 4 = 3

 Bentuk alog (b/c) = alog b - alog c
Contoh :
2
log (16/2) = 2log 16 - 2log 2 = 4 - 1 = 3
4

log (32/2) = 4log 32 - 4log 2 = 4log 16 + 4log 2 - 4log 2 = 4log 16 = 2

 Bentuk alog (b/c) = - alog (c/b)
Contoh :
2
log (4/2) = - 2log (2/4) = - 2log ½ = - 2log 2-1 = -(-1) 2log 2 = 1
4

log (32/2) = - 4log (2/32) = - 4log (1/16) = - 4log 4-2 = -(-2) 4log 4 = 2

 Bentuk alog bm = m . alog b
Contoh :
2
log 4 = 2log 22 = 2 2log 2 = 2.1 = 2
2

log √32 = 2log (25)½ = 2log 25/2 = 5/2 . 2log 2 = 5/2 (1) = 5/2

2

log 84 = 4 2log 8 = 2 . 3 = 6

 Bentuk anlog bm = m/n . alog b
Contoh :
22
log 43 = 3/2 . 2log 4 = 3/2 (2) = 3
24

log √32 = 24log 32½ = 1/8 . 2log 32 = 1/8 (5) = 5/8

 Bentuk alog b . blog c . clog d = alog d
Contoh :
2
log 4 . 4log 16 = 2log 16 = 2log 24 = 4
2

log 4 . 4log 16 16log 4 = 2log 4 = 2log 22 = 2

(2log 4 + 2log 6) . 24log 32 = 2log (4.6) . 24log 32 = 2log 32 = 5