In logarithms, there are three fundamental power rules and here is the list of properties which represent formulas of power of the logarithms in algebraic form with proofs.

1.

The logarithm of an exponential function to a number is equal to the product of the exponent of the exponential term and logarithm of base of the exponential term to the number.

$\large \log_{b} m^x = x \log_{b} m$

2.

The logarithm of a number to an exponential function is equal to the product of reciprocal of the exponent of the base and logarithm of the number to base of the exponential term.

$\large \log_{b^y} m = \Big(\dfrac{1}{y}\Big) \log_{b} m$

3.

The logarithm of an exponential function to another exponential term is equal to the product of the quotient of exponents of number by the base and logarithm of the base of the number to base of the base exponential term.

$\large \log_{b^y} m^x = \Big(\dfrac{x}{y}\Big) \log_{b} m$

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

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

Jun 23, 2018

Limit (Calculus)

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

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

Jun 21, 2018

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Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

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