Tolong Dijawab Materi : Logaritma Kelas. : 10 SMK

a.
²log45 = ²log(9 x 5)
= ²log(3² x 5)
= ²log3² + ²log5
= 2. ²log3 + ²log5
= 2.a + b

b.
²⁵log36 = ²log36 / ²log25
= ²log(9x4) / ²log5²
= ²log(3² x 2²) / ²log5²
= (²log3² + ²log2²) / ²log5²
= (2. ²log3 + 2. ²log2) / 2 . ²log5
= (2.a + 2.1) / 2.b
 = 2(a + 1) / 2b
= (a+1) / b

c.
³⁰log150 = ²log150 / ²log30
= ²log(2 x 3 x 25) / ²log(2 x 3 x 5)
= ²log(2 x 3 x 5²) / ²log(2 x 3 x 5)
= (²log2 + ²log3 + 2 . ²log5) / (²log2 + ²log3 + ²log5)
= (1 + a + 2.b) / (1 + a + b)

d.
¹⁰⁰log50 = ²log50 / ²log100
= ²log(25 x 2) / ²log(25 x 4)
= ²log(5² x 2) / ²log(5² x 2²)
= (²log5² + ²log2) / (²log5² + ²log2²)
= (2 . ²log5 + ²log2) / (2. ²log5 + 2 . ²log2)
= (2 . b + 1) / (2 . b + 2 . 1)
= (2b + 1) / (2b + 2)

e.
⁴log75 = ²log75 / ²log4
= ²log(25 x 3) / ²log2²
= (²log5² + ²log3) / 2 . ²log2
= (2 . ²log5 + ²log3) / 2 . 1
= (2 . b + a) / 2
= (a + 2b) / 2

LogAritMa

2'log 3 = a
2'log 5 = b

3'log 5 = 2'log 5 / 2'log 3 = b/a

2'log 45
= 2'log (3² × 5)
= 2 . 2'log 3 + 2'log 5
= 2a + b

25'log 36
= 5²'log 6²
= 5'log 6
= 5'log (2 × 3)
= 5'log 2 + 5'log 3
= 1/b + a/b
= (1 + a)/b

30'log 150
= 2'log 150 / 2'log 30
= 2'log (2 × 3 × 5²) / 2'log (2 × 3 × 5)
= [2'log 2 + 2'log 3 + 2 . 2'log 5] / [2'log 2 + 2'log 3 + 2'log 5]
= (1 + a + 2b)/(1 + a + b)

100'log 50
= 2'log (100/2) / 2'log 100
(2'log 100 - 2'log 2) / 2'log 100
= 1 - 1/2'log 100
= 1 - 1/(2'log (2² × 5²)
= 1 - 1/(2 + 2b)
= (1 + 2b)/(2 + 2b)

4'log 75
= 4'log (3 × 5²)
= 2²'log 3 + 2²'log 5²
= 1/2 . 2'log 3 + 2'log 5
= 1/2 a + b