Properties of Logarithms

$$\frac{\log\left(x\right)}{\log\left(y\right)}$$  

$$\frac{\log\left(y\right)}{\log\left(x\right)}$$  

$$\frac{\ln\left(y\right)}{\ln\left(x\right)}$$  

$$\frac{\ln\left(x\right)}{\ln\left(y\right)}$$  

$$\log_b\left(yx\right)=\log_b\left(y\right)\ -\ \log_b\left(x\right)$$  

$$\log_b\left(\frac{x}{y}\right)=\log_b\left(x\right)+\log_b\left(y\right)$$  

$$\log_b\left(xy\right)=\log_b\left(x\right)+\log_b\left(y\right)$$  

$$\log_b\left(\frac{x}{y}\right)=\log_b\left(x\right)-\log_b\left(y\right)$$  

$$\log_b\left(yx\right)=\log_b\left(y\right)\ -\ \log_b\left(x\right)$$  

$$\log_b\left(\frac{x}{y}\right)=\log_b\left(x\right)+\log_b\left(y\right)$$  

$$\log_b\left(\frac{x}{y}\right)=\log_b\left(y\right)-\log_b\left(x\right)$$  

$$\log_b\left(\frac{x}{y}\right)=\log_b\left(x\right)-\log_b\left(y\right)$$  

$$\log_b\left(x\right)^y=x\log_b\left(y\right)$$  

$$\log_b\left(x\right)^y=\log_by\left(x\right)$$  

$$\log_b\left(x\right)^y=y\log_b\left(x\right)$$  

$$\log_b\left(x^y\right)=\left(\log_b\left(x\right)\right)^y$$  

$$\log_xx=0$$  

In the logarithm $$\log_xy$$  , y can be a negative number

$$\log_x1\ =0$$  

A logarithm can never equal zero

False

True

Change of Base

Power Rule

Quotient Rule

Power Rule

Product Rule

Power Rule Product Rule

The one/identity/unit Property

The Zero Property

Power Rule

Product Rule

Power Rule

Quotient Rule

Power Rule

Product Rule

Quotient Rule

Power Rule Product Rule

Change of Base Formula

Power Rule

Product Rule

$$\log_7\left(x\right)$$  

$$\log_{10}\left(x\right)$$  

$$\log_e\left(x\right)$$  

$$\log\left(x\right)$$  

It is a variable

It is a number equal to 2.7...