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.

The change of base logarithm formula in division form.

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

The change of base logarithm formula in product form.

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

The change of base logarithm formula in reciprocal form.

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

List of most recently solved mathematics problems.

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Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

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Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

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Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

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