Question

Kerjakan dengan menggunakan sifat-sifat logaritma
1. 2 log 24 - 8 log 27
2. 2^3 log 4 -1/2 3 log 25 + 3 log 10 - 3 log 32
3. 3 log 5 X 25 log 27

Answer 1

1. 2log 24 - 8log 27
= 2log 24 - 2³log 3³
= 2log 24 - 3/3 2log3
= 2log 24 - 2log3
= 2log (24/3)
= 2log 8 = 3

2. 2³log4 - 1/2 3log25 + 3log10 - 3log32
= 2³log2² - 3²log5² + 3log10 - 3log32
= 2/3 2log2 - 2/2 3log5 + 3log10 - 3log32
= 2/3 - 3log(5*10/32)
= 2/3 - 3log(50/32)
= 2/3 - 3log(25/16)
= 2/3 - 3log(5/4)²

3. 3log5 * 25log27
= 3log5 * 5²log3³
= 3log5 * 3/2 5log3
= 3/2 * 3log5 * 5log3 = 3/2* 1 = 3/2