Properties logarithmic functions

Introduction: The properties of exponential functions (See Properties exponential functions) correspond to 'mirrored' properties of logarithmic functions.

Theorem: Properties of logarithmic functions: (For ease of notation we have omitted the base.)

1. $\log (x\cdot y)=\log x+\log y$
2. $\log {\displaystyle\frac{x}{y}}=\log x-\log y$
3. $\log x^y=y\log x$
4. $\log 1=0$