LOGARITMA
- Jika log 5 = 0,699 dan log 3 = 0,477 , maka log 150 = ………….
Jawab : log 150 = log (5 x 3 x 10)
= log 5 + log 3 + log 10
= 0,699 + 0,477 + 1
= 2,176
- Nilai dari 5 log 10 + 5 log 50 – 5 log 4 = …………
Jawab : 5 log (10 x 50)
4
5 log (500)
4
5 log 125 = y
125 = 5 y
5 ³ = 5 y
y = 3
- Nilai x yang memenuhi persamaan 2 log (x – 2) + 2 log (x – 3) = 2 log 3 . 3 log 2 adalah …………
Jawab : 2 log (x – 2) (x – 3) = 2 log 2
(x – 2) (x – 3) = 2
x ² - 5 x + 6 – 2 = 0
(x – 1) = 0 (x – 4) = 0
x – 1 = 0 x – 4 = 0
x = 1 / x = 4
- Jika a log 81 – 2a log 27 + a log 243 = 6, maka nilai a = …………..
Jawab : a log 81 – 2a log 27 + a log 243 = 6
a log 81 – a log 27 ² + a log 243 = 6
a log (81 . 243) = 6
27²
a log (3⁴ x 3⁵) = 6
3³·²
a log (3 ⁽⁴⁻⁶⁺⁵⁾) = 6
a log 3³ = 6
a⁶ = 3³
a = 3½
- Jika log 2 = p dan log 3 = q, maka log 12 = ………….
Jawab : log 12 = log (2² x 3)
= log 2² + log 3
= 2p + q
- Nilai dari 2 log16 – 3 log 27 + 5 log 1 = …………………
Jawab : 2 log 16 – 3 log 27 + 5 log 1
= 4 - 3 + 0
= 1
- Nilai x dari log (x + 1) = 1 + log x adalah …………….
Jawab : log (x + 1) = 1 + log x
log (x + 1) = log 10 + log x
log (x + 1) = log (10 . x)
x + 1 = 10 x
x – 10 x = -1
-9 x = -1
x = 1/9
- Nilai dari log 2 √2 + log √3 + log 18 = ……………………
log 6
Jawab : log 2 √2 + log √3 + log 18
log 6
= log (2 √2 . √3 . 18)
log 6
= log (36 √6)
log 6
= log (6² . 6½)
log 6
= log (6²⁺¹ ²)
log 6
= log 6⁵ ²
log 6
= 5/2 log 6
log 6
= 5/2
- Jika log x² - log x + log √x = 6, maka x = ………………….
Jawab : log x² - log x + log √x = 6
log (x² . x ¹ ²) = 6
x
log (x ⁽²⁺¹ ²⁻¹⁾) = 6
log . x³ ² = 6
10⁶ . x³ ² = 0
x = 10 . ⁶/₃ ₂
x = 10⁶ · ² ³
x = 10⁴
x = 10.000
- Nilai dari 2 log 3 . 3 log 5 . 5 log 6 . 6 log 8 = …………....
Jawab : 2 log 3 . 3 log 5 . 5 log 6 . 6 log 8
= 2 log 5 . 5 log 8
= 2 log 8
= 3
- Jika 4 log 5 = a, maka 16 log √5 = ………….
Jawab : 16 log √5
= 4² log 5¹ ²
= ½ . 4 log 5
2
= ½ . ½ . a
= ¼ a
- Nilai 2 log 40 – 2 log 5 + 2 log 4 = …………
Jawab : 2 log 40 – 2 log 5 + 2 log 4
= 2 log (40 . 4)
5
= 2 log 160
5
= 2 log 32
= 5
PERSAMAAN LINIER
- Tentukan persamaan garis yang melalui titik P (5, -3) dan Q (-1, -4)
Jawab : m = y₂ - y₁
x₂ - x₁
m = -4 – (-3) = -1 = 1/6
-1 – 5 -6
y – y₁ = m (x - x₁)
y – (-4) = 1/6 (x – (-1))
y = 1/6x + 1/6 - 4
y = 1/6x – 23/6
6y = x – 23
x = 6y + 23 y = -23/6
x = 23 y = -3,83
- Harga 5 baju Rp. 50.000,- dan harga 3 baju Rp. 25.000,-. Berapakah harga 10 baju ?
Jawab : x = baju y = harga
x₁ = 5 y₁ = 50.000
x₂ = 3 y₂ = 25.000
m = - 25.000 = 12.500
- 2
y - y₁ = m (x - x₁)
y – 50.000 = 12.500 (x – 5)
y = 12.500x – 62.500 + 50.000
y = 12.500x – 12.500
10 baju = 12.500 (10) – 12.500
= 125.000 – 12.500
= 112.500
- Tentukan persamaan garis yang melalui titik A (5, -4) dan B (-5, 1)
Jawab : m = y₂ - y₁
x₂ - x₁
m = 1 + 4 = 5 = -1/2
-5 - 5 -10
y – y₁ = m (x - x₁)
y – (-4) = -1/2 (x - 5)
y = -1/2x + 5/2 - 4
y = -1/2x – 3/2
2y = -x – 3
x = -2y – 3 y = -3/2
x = -3 y = -1,5
- Harga 15 buku Rp. 35.000,- dan harga 8 buku Rp. 14.000,-. Berapakah harga 13 baju ?
Jawab : x = buku y = harga
x₁ = 15 y₁ = 35.000
x₂ = 8 y₂ = 14.000
m = - 21.000 = 3.000
- 7
y - y₁ = m (x - x₁)
y – 35.000 = 3.000 (x – 15)
y = 3.000x – 45.000 + 35.000
y = 3.000x – 10.000
8 buku = 3.000 (13) – 10.000
= 39.000 – 10.000
= 29.000
- Tentukan persamaan garis yang melalui titik R (-2, -3) dan S (-3, 6)
Jawab : m = y₂ - y₁
x₂ - x₁
m = 6 + 3 = 9 = -9
-3 + 2 -1
y – y₁ = m (x - x₁)
y – (-3) = -9 (x – (-2))
y = -9x - 18 - 3
y = -9x - 21
9x + 21 = 0
9x = -21
x = -21/9
x = -2,3 y = -21
- Harga 2 kg telur Rp. 45.000,- dan harga 6 kg telur Rp. 105.000,-. Berapakah harga 1 kg telur ?
Jawab : x = telur y = harga
x₁ = 2 y₁ = 45.000
x₂ = 6 y₂ = 105.000
m = 60.000 = 15.000
4
y - y₁ = m (x - x₁)
y – 45.000 = 15.000 (x – 2)
y = 15.000x – 30.000 + 45.000
y = 15.000x + 15.000
1 kg telur = 15.000 (1) + 15.000
= 30.000
- Tentukan persamaan garis yang melalui titik K (-6, 1) dan L (5, 2)
Jawab : m = y₂ - y₁
x₂ - x₁
m = 2 - 1 = 1
5 + 6 11
y – y₁ = m (x - x₁)
y – 1 = 1/11 (x + 6)
y = 1/11x + 6/11 + 1
y = 1/11x + 17/11
11y = x + 17
x = 11y - 17 y = 17/11
x = -17 y = 1,55
- Harga 7 penghapus Rp. 14.000,- dan harga 13 buku Rp. 38.000,-. Berapakah harga 25 penghapus ?
Jawab : x = penghapus y = harga
x₁ = 7 y₁ = 14.000
x₂ = 13 y₂ = 38.000
m = 24.000 = 4.000
6
y - y₁ = m (x - x₁)
y – 14.000 = 4.000 (x – 7)
y = 4.000x – 28.000 + 14.000
y = 4.000x – 14.000
25 penghapus = 4.000 (25) – 14.000
= 100.000 – 14.000
= 86.000
- Tentukan persamaan garis yang melalui titik M (4, -2) dan N (-2, 8)
Jawab : m = y₂ - y₁
x₂ - x₁
m = 8 + 2 = 10
-2 - 4 -6
y – y₁ = m (x - x₁)
y + 2) = -10/6 (x – 4)
y = -10/6x + 40/6 - 2
y = -10/6x + 28/6
6y = -10x + 28
10x – 28 = 0
10x = 28
x = 28/10 y = 28/6
x = 0,28 y = 4,67
- Harga 17 penggaris Rp. 32.000,- dan harga 9 penggaris Rp. 20.000,-. Berapakah harga 5 penggaris ?
Jawab : x = penggaris y = harga
x₁ = 17 y₁ = 32.000
x₂ = 9 y₂ = 20.000
m = - 12.000 = 1.500
- 8
y - y₁ = m (x - x₁)
y – 32.000 = 1.500 (x – 17)
y = 1.500x – 25.500 + 32.000
y = 1.500x + 6.500
8 buku = 1.500 (5) + 6.500
= 7.500 + 6.500
= 14.000
Tidak ada komentar:
Posting Komentar