**5.2b Penukaran Asas Logaritma**

$$\overline{)\begin{array}{l}\text{}{\mathrm{log}}_{a}b=\frac{{\mathrm{log}}_{c}b}{{\mathrm{log}}_{c}a}\text{}\\ \text{dan}\\ \text{}{\mathrm{log}}_{a}b=\frac{1}{{\mathrm{log}}_{b}a}\text{}\end{array}}$$

**Contoh 1:**

Cari nilai-nilai yang berikut:

(a) log

_{25}100(b) log

_{3}0.45

*Penyelesaian:*$\begin{array}{l}\text{(a)}{\mathrm{log}}_{25}100\\ =\frac{{\mathrm{log}}_{10}100}{{\mathrm{log}}_{10}25}=\frac{10}{1.3979}=7.154\\ \\ \text{(b)}{\mathrm{log}}_{3}0.45\\ =\frac{{\mathrm{log}}_{10}0.45}{{\mathrm{log}}_{10}3}=\frac{-0.3468}{0.4771}=-0.727\end{array}$

**Contoh 2:**

Cari nilai-nilai yang berikut:

(a) log

(b) log

(c) log

(d) log

(a) log

_{4 }8(b) log

_{125}5(c) log

_{81}27(d) log

_{16}64

*Penyelesaian:*