Muhammad Erfan

Sifat-sifat Logaritma

1. $^{a}log \; 1 = 0$
2. $^{a} log \; a = 1$
3. $y = ^{a} log \; x \Leftrightarrow x = a^{y}$
4. $a^{{}^{a} log \; x} = x$
5. ${}^{a} log \left(x \cdot y \right) = {}^{a} log \, x + {}^{a} log \, y$
6. ${}^{a} log \left(\frac{x}{y} \right) = {}^{a} log \, x - {}^{a} log \, y$
7. ${}^{a} log \left(x^{n} \right) = n \cdot {}^{a} log \, x$
8. ${}^{a} log \, x = \frac{{}^{b} log \, x}{{}^{b} log \, a}$
9. ${}^{a} log \, x = \frac{1}{{}^{x} log \, a}$
10. ${}^{a^{n}} log \, x^{m} = \frac{m}{n} \cdot {}^{a} log \, x$
11. $log \, x = {}^{10} log \, x$
12. Jika $e=2,71828...$ merupakan bilangan natural, maka: ${}^{e} log \, x = ln \, x$
13. $colog \, x = log \frac{1}{x} = -log \, x$
14. ${}^{a} log \, b \cdot {}^{b} log \, c \cdot {}^{c} log \, d \cdot {}^{d} log \, f = {}^{a} log \, f$

Contoh Soal:

Diketahui:

$$ \begin{align*} A &= \frac{2}{{}^{11} log \, 385} + \frac{2}{{}^{7} log \, 385} + \frac{2}{{}^{5} log \, 385} \end{align*} $$