__Example 1__Express the following in term of ${\mathrm{log}}_{a}x$ and ${\mathrm{log}}_{a}y$ .

(a) ${\mathrm{log}}_{a}3x$

(b) ${\mathrm{log}}_{a}\frac{x}{5}$

(c) ${\mathrm{log}}_{a}{y}^{5}$

(d) ${\mathrm{log}}_{a}x{y}^{3}$

(e) ${\mathrm{log}}_{a}\frac{{x}^{2}}{\sqrt{y}}$

(f) ${\mathrm{log}}_{a}\sqrt{\frac{y}{{a}^{2}{x}^{3}}}$

*Law of Logarithms*