Soal-Soal Matematika/Eksponen dan logaritma
Bentuk dan sifat eksponen
[sunting]bentuk: ab = c
sifat:
- amxan = am+n
- am:an = am-n
- (am)n = amxn
- = am/n
- amxbm = (axb)m
- am:bm = (a:b)m
- a-m =
- amn = a(mn)
- (am)n ≠ amn
- 0a = 0 dengan a > 0
- a0 = 1 dengan a ≠ 0
- 0:a = 0 dengan a ≠ 0
- a1 = a
- a-1 = dengan a ≠ 0
- aa = bb dimana a = b
- Tambahan
- xx……n = n maka dengan x ≥ 1
- xxn = n maka x = n dengan x ≥ 1
Bentuk dan sifat logaritma
[sunting]bentuk: alog c = b dengan {a,c} > 0 dan a ≠ 1
sifat:
- log a+log b = log (axb)
- log a-log b = log (a:b)
- log a:log b = blog a
- blog a x alog c = blog c
- blog a = log a:log b
- blog a = 1:alog b
- = a
- blog am = m x blog a
- = 1/n blog a
- = m/n blog a
- alog 1 = 0
- alog a = 1
contoh soal
Berapa nilai x dari
- x2x6 = 36
- xx2 = 16
- 6x + x = 219
- 2x + 2x = 8
- 3x + 5x = 101
- jawaban
- x2x6 = 36
- x2x6 = 62
- (x2x6)3 = (62)3
- (x6)x6 = 66
- x6 = 6
- xx2 = 16
- xx2 = 42
- (xx2)2 = (42)2
- (x2)x2 = 44
- x2 = 4
- 6x + x = 219
- 6x = 219 - x
- 6219 x 6x = (219 - x) 6219
- 6219 = (219 - x) 6(219 - x)
- 63 x 6216 = (219 - x) 6(219 - x)
- 216 x 6216 = (219 - x) 6(219 - x)
- 216 = 219 - x
- x = 3
- 2x + 2x = 8
- 2x = 8 - 2x
- 2x = 2(4 - x)
- 24 x 2x = 2(4 - x) 24
- = (4 - x) 2(4 - x)
- 23 = (4 - x) 2(4 - x)
- 2 x 22 = (4 - x) 2(4 - x)
- 2 = 4 - x
- x = 2
- 3x + 5x = 101
- 3x = 101 - 5x
- 3x = 5( - x)
- 3 x 3x = 5( - x) 3
- = ( - x) 3( - x)
- 3 3 = ( - x) 3( - x)
- 34 3 = ( - x) 3( - x)
- x 3 = ( - x) 3( - x)
- = - x
- x =
- x =
- x = 4