soal log

^{1. 3}Log 3 = ……

Jawab :

          ^aLog a  = 1

maka, ³Log 3  = 1

^{2. 3}Log 27 = ……

Jawab :

³Log 27 = ³Log 3³ = 3 X ³Log 3 = 3 X 1 = 3

^{3. 2}Log 1/243 X ⁵Log 1/125 X ³Log 1/16= ………...

Jawab :

= ²Log 1/243 X ⁵Log 1/125 X ³Log 1/16

= ²Log 243^-1 X ⁵Log 125^-1 X ³Log 16^-1

= ²Log 3^-5 X ⁵Log 5^-3 X ³Log 2^-4

= -5  ²Log 3 X -3 ⁵Log 5 X -4  ³Log 2

= -5  ²Log 3 X -4  ³Log 2 X -3 ⁵Log 5

= -5 X -4 ( ²Log 3 X ³Log 2 ) X -3 X 1

= 20 ²Log 2 X -3 X 1

= 20 X 1 X -3 X 1

= -60

^{4. 2}Log 64 + ²Log 6 - ²Log 24

Jawab :

= ²Log 2⁶ + ²Log (2 X 3) - ²Log (2³ X 3)

= 6  ²Log 2 + ²Log 2 + ²Log 3 - (3  ²Log 2 + ²Log 3)

= 6  ²Log 2 + ²Log 2 + ²Log 3 - 3  ²Log 2 - ²Log 3

= 6 X 1 + 1 + ²Log 3 - 3 X 1 - ²Log 3

= 6 + 1 - 3 + ²Log 3 - ²Log 3

= 4

^{5. 25}Log 5^2a = 8

Maka a = …….

Jawab :

²⁵Log 5^2a       = 8

25⁸             = 5^2a

25⁸              = (5²)^a

25⁸             = 25^a

8                 = a

6. Log a = 1/3 Log 8 + Log 9 – 1/3 Log 27

a= ……..  

Jawab  :  

Log a = 1/3 Log 8 + Log 9 – 1/3 Log 27

Log a = 1/3 Log 2³ + Log 3² – 1/3 Log 3³

Log a = 3/3 Log 2 + 2 Log 3 – 3/3 Log 3

Log a = Log 2 + 2 Log 3 – Log 3

Log a = Log 2 + Log 3

Log a = Log (2 X 3)

Log a = Log 6

a        = 6