**5.2a Hukum-hukum Logaritma**

$$\overline{)\begin{array}{l}\text{Hukum1:}\\ {\text{log}}_{a}xy={\text{log}}_{a}x+{\text{log}}_{a}y\\ \\ \text{Contoh:}\\ \text{}{\mathrm{log}}_{5}25x={\text{log}}_{5}25+{\text{log}}_{5}x\\ \\ \text{Berhati-hati!!}\\ {\text{log}}_{a}x+{\text{log}}_{a}y\ne {\text{log}}_{a}\left(x+y\right)\text{}\end{array}}$$

$$\overline{)\begin{array}{l}\text{Hukum2:}\\ {\text{log}}_{a}\left(\frac{x}{y}\right)={\text{log}}_{a}x-{\text{log}}_{a}y\text{}\\ \\ \text{Contoh:}\\ \text{}{\mathrm{log}}_{5}\frac{x}{25}={\text{log}}_{5}x-{\text{log}}_{5}25\\ \\ \text{Berhati-hati!!}\\ {\text{log}}_{a}\frac{x}{y}\ne \frac{{\text{log}}_{a}x}{{\text{log}}_{a}y}\text{}\end{array}}$$

$$\overline{)\begin{array}{l}\text{Hukum3:}\\ {\text{log}}_{a}{x}^{m}=m{\text{log}}_{a}x\\ \\ \text{Contoh:}\\ \text{}{\mathrm{log}}_{5}{y}^{5}=5{\text{log}}_{5}y\\ \\ \text{Berhati-hati!!}\\ \text{}{\left({\text{log}}_{a}x\right)}^{2}\ne 2{\text{log}}_{a}x\text{}\end{array}}$$

**Contoh 1:**

Ungkapkan setiap yang berikut dalam bentuk log

*dan log*_{a }x_{a}*y*.$\begin{array}{l}\text{(a)}{\mathrm{log}}_{a}3x\\ \text{(b)}{\mathrm{log}}_{a}\frac{x}{5}\\ \text{(c)}{\mathrm{log}}_{a}{y}^{5}\\ \text{(d)}{\mathrm{log}}_{a}x{y}^{3}\\ \text{(e)}{\mathrm{log}}_{a}\frac{{x}^{2}}{\sqrt{5}}\\ \text{(g)}{\mathrm{log}}_{a}\sqrt{\frac{y}{{a}^{2}{x}^{3}}}\end{array}$

*Penyelesaian:*