WISKUNDE
GRAAD 12
NOG OEFENINGE
Logaritme : antwoorde.
MATHEMATICS
GRADE 12
MORE EXERCISES
Logarithm : answers.
1.1
y = 2x : log2 y = x
1.2
y = 5x : log5 y = x
1.3
49 = 72 : log7 y = 2
1.4
81 = 34 : log3 81 = 4
1.5
y = (1/2)x : log(1/2) y = x
1.6
y = (1/7)x : log(1/7) y = x
2.1
y = logb x : x = by
2.2
a = logb c : c = ba
2.3
y = log2 x : x = 2y
2.4
y = log(1/2) x : x = (1/2)y
2.5
log3 9 = 2 : 9 = 32
2.6
log(1/2) 8 = −3 : 8 = (1/2)−3
2.7
log 100 = 2 : 100 = 102
2.8
log x = y : x = 10y
3.1
2x = 5
3.2
4x = 18
log 2x = log 5 neem / take logs
log 4x = log 18
x log 2 = log 5 log ab = b log a
x log 4 = log 18
log 5
log 18
x = ────
x = ─────
log 2
log 4
= 2,32
= 2,08
3.3
3x − 2 = 8
3.4
7x + 1 = 13
log 3x − 2 = log 8
log 7x + 1 = log 13
(x − 2) log 3 = log 8
(x + 1) log 7 = log 13
log 8
log 13
x− 2 = ────
x + 1 = ─────
log 3
log 7
= 1,89298....
= 1,31812...
x = 3,89
x = 0,32
3.5
3.5x = 10
3.6
7x = 114.6x
10
7x
5x = ───
─── = 114
3
6x
┏
┓x
10
┃ 7
┃
log 5x = ───
┃──┃ = 114
3
┃ 6
┃
┗
┛
log (10/3)
log 114
x = ───────
x = ───────
log 5
log (7/6)
= 0,75
= 30,72
3.7
3x.9 x + 1 = 36
3.8
26.(1,125)x = 312
3x.9x.91 = 36
(1,125)x = (312 ÷ 26)
3x.32x = 4
(1,125)x = 12
3x log 3 = log 4
x log 1,125 = log 12
log 4
log 12
3x = ───
x = ───────
log 3
log 1,125
= 1,26185....
= 21,10
x = 0,42
4.
Pas die logaritmiese wette toe.
4.
Apply the logaritmic laws.
x
(1) : logb xy = logb x + logb y
(2) : logb ── = logb x − logb y
y
log x
(3) : logb x y = y logb x
(4) : logy x = ────
log y
4.1
log 6 = log (2 x 3)
4.2
log 25 = log 52
= log 2 + log 3 . . . wet/law 1
= 2log 5 . . . wet/law 2
= a + b
= 2c
4.3
log 15 = log (3 x 5)
4.4
log 18 = log (2 x 32)
= log 3 + log 5 . . . wet/law 1
= log 2 + 2log 3 . . . wet/law 1, 2
= b + c
= a + 2b
4.5
log 12 = log (22 x 3)
4.6
log 2,5 = log (5 ÷ 2)
= 2log 2 + log 3 . . . wet / law 1, 2
= log 5 − log 2 . . . wet / law 3
= 2a + b
= c − a
4.7
log 1,2 = log (2 x 3 ÷ 5)
4.8
log 45 = log (32 x 5)
= log 2 + log 3 − log 5 . . . wet / law 1,2
= 2log 3 + log 5 . . . wet / law 1,3
= a + b − c
= 2b + c
4.9
log 7,5 = log (3 x 5 ÷ 2)
4.10
log 36 = log (22 x 32)
= log 3 + log 5 − log 2 . . . wet / law 1,2
= 2log 2 + 2log 3 . . . wet / law 1,3
= b + c − a
= 2(a + b)
4.11
log 40 = log (23 x 5)
4.12
log 375 = log (3 x 53)
= 3log 2 + log 5 . . . wet / law 1,3
= log 3 + 3log 5 . . . wet / law 1,3
= 3a + c
= b + 3c
log 2
log 5
4.13
log 3 2 = ───── . . . wet / law 4
4.14
log 2 5 = ───── . . . wet / law 4
log 3
log 2
a
c
= ──
= ──
b
a
log (2 x 3)
log (5 ÷ 2)
4.15
log 5 6 = ─────── . . . wet / law 4
4.16
log 3 2,5 = ─────── . . . wet / law 4
log 5
log 3
log 2 + log 3
log 5 − log 2
= ────────── . . . wet / law 1
= ────────── . . . wet / law 2
log 5
log 3
a + b
c − a
= ─────
= ─────
c
b