6

3

9

27

$$\log_ab^{\alpha}=\alpha\log_ab$$

$$\log_a\frac{1}{b}=-\log_ab$$

$$\log_ab=\frac{\log_cb}{\log_ca}$$

$$\log_{a^{\alpha}}b=\frac{1}{\alpha}\log_ab$$

$$\log_5\left(1-\sqrt{3}\right)^4=4\log_5\left(1-\sqrt{3}\right)$$

$$\log_5\left(1-\sqrt{3}\right)^4=-4\log_5\left(\sqrt{3}-1\right)$$

$$\log_5\left(1-\sqrt{3}\right)^4=4\log_5\left(\sqrt{3}-1\right)$$

$$\log_5\left(1-\sqrt{3}\right)^4=\frac{1}{4}\log_5\left(1-\sqrt{3}\right)$$

$$\frac{a+1}{a+b}$$  

$$2$$  

$$\frac{3}{a+b}$$  

$$\frac{a+b}{a}$$  

$$\log_3^2a^2=2\log_3^2a$$

$$\log_3^2a^2=4\log_3^2\left|a\right|$$

$$\log_3^2a^2=4\log_3^2a$$

$$\log_3^2a^2=2\log_3^2\left|a\right|$$

$$a^4.b^6$$  

$$a^2.b^{14}$$  

$$a^6.b^{12}$$  

$$a^8.b^{14}$$  

$$.Q=b^{-\frac{4}{3}}$$  

$$Q=b^2$$  

$$Q=b^{\frac{4}{3}}$$  

$$Q=b^{\frac{5}{9}}$$  

$$\log⁡_a\frac{x}{y}=\log⁡_ax-\log⁡_ay$$  

$$\log⁡_a\frac{x}{y}=\log⁡_a(x-y)$$  

$$\log⁡_a\frac{x}{y}=\log⁡_ax+\log⁡_ay$$  

$$\log⁡_a\frac{x}{y}=\frac{\log⁡_ax}{\log⁡_ay}$$  

$$a^m+a^n=a^{m+n}.$$  

$$a^m.a^n=a^{m-n}$$  

$$.\frac{a^m}{a^n}=a^{n-m}.$$  

$$(a^m)^n=(a^n)^m.$$