contoh soal logaritma dan sifatnya

 1. Tentukan nilai dari: 2log 8 + 3log 9 + 5log 125

= 2log 23 + 3log 32 + 5log 53 = 3 2log 2 + 2 3log 3 + 3 5log 5

= 3 + 2 + 3 = 8

2.  2log 1/8 + 3log 1/9 + 5log 1/125

= 2log 2−3 + 3log 3−2 + 5log 5−3

= − 3 − 2 − 3 = − 8

3. Tentukan nilai dari:

√2log 8

= 21/2log 23 = 3/0,5 2log 2 = 3/0,5 = 6 

4. √3log 9

= 31/2log 32 = 2/0,5 3log 3 = 2/0,5 = 4

5. Tentukan nilai dari

4log 8 + 27log 9

= 22log 23 + 33log 32

= 3/2 2log 2 + 2/3 3log 3 

= 3/2 + 2/3 = 9/6 + 4/6 = 13/6

6. 8log 4 + 27log 1/9

23log 22 + 33log 3−2

= 2/3 2log 2 + (−2/3) 3log 3 

= 2/3 − 2/3 = 0

7. 9 log 4 / 3 log 7

= 3^2 log 22 / 3 log 7

= 3 log 2 / 3 log 7

= 7 log 2

8. 9^(3 log 7)

= 32 ^(3 log 7)

= 3^(2 .3 log 7)

= 3^(3 log 49)

= 49

 9. 2 log 25 . 5 log 4 + 2 log 6 – 2log 3

2 log 52 . 5 log 22 + 2 log (3.2/3)

= 2.2 . 2 log 5 . 5 log 2+ 2 log 2

= 2 . 2 log 2 + 1

= 2 . 1 + 1

= 3