Logarithmic Properties

Quotient Property

Equality Property

Power Property

Product Property

$$\log_x\left(4x\right)\ =\ \log_x\left(5x+2\right)$$  

$$\log_5\left(125\right)\ =\ \log_5\left(25\right)\ +\ \log_5\left(5\right)$$  

$$\log_48^{2\ }=\ 2\log_48$$  

$$\log_xy\ =\ \log_xw$$  

Product Property

Power Property

Quotient Property

Equality Property

Power rule applies

2x+1 = 7

$$7\log_2x\ =\ 2x+1$$  

No solution

$$\log_x\left(\frac{5}{1+x}\right)\ =\ \log_x5\ -\ \log_x\left(1+x\right)$$  

$$\log_x3x\ =\ \log_x3\ +\ \log_xx$$  

$$\log_xy\ +\ \log_x2y\ =\ \log_x2y^2$$  

$$\log_x2y^2\ =\ 2\log_x2y$$