Change of Base Logarithm formulas

The rule of changing the base of a logarithmic term is called the change of base rule of logarithmic term. In logarithms, the base of any logarithm term can be changed in three ways and they are used as change of base formulas in logarithms.

Change of Base Rule

The change of base logarithm formula in division form.

$\large \log_{b}{m} = \dfrac{\log_{d}{m}}{\log_{d}{b}}$

Product form

The change of base logarithm formula in product form.

$\large \log_{b} m = \log_{a} m \times \log_{b} a$

Switch Rule

The change of base logarithm formula in reciprocal form.

$\large \log_{b}{m} = \dfrac{1}{\log_{m}{b}}$