Properties of Logarithms

Category : 9th Class

*         Properties of Logarithms

 

  •   \[{{\log }_{a}}(xy)={{\log }_{a}}x+{{\log }_{a}}y\]
  •   \[{{\log }_{x}}x=1\]
  •   \[{{\log }_{a}}{{x}^{n}}=n{{\log }_{a}}x\]
  •   \[{{\log }_{a}}x=\frac{1}{{{\log }_{x}}a}\]
  •   \[{{\log }_{a}}\left( \frac{x}{y} \right)={{\log }_{a}}x-{{\log }_{a}}y\]
  •   \[{{\log }_{a}}x=\frac{{{\log }_{b}}x}{{{\log }_{b}}a}\]  

The last formula given above is also known as base changing formula.  

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