Quantity and/or base quantity of logarithmic terms can be expressed in exponential form to find the values of logarithm of quantities. Due to the involvement of exponents in logarithms, the logarithmic identities are simply called as power rules of logarithms.

There are three power rules in logarithms and they are used as formulas in logarithmic mathematics to find the values of logarithmic terms easily.

Logarithm of a quantity in exponential form is equal to the product of exponent and logarithm of base of exponential term.

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

Logarithm of a quantity to a base in exponential form is equal to the quotient of logarithm of quantity by the exponent of base quantity in exponential form.

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

Logarithm of a quantity in exponential form to a base in exponential form is equal to product of quotient of exponent of quantity by the exponent of base quantity and logarithm of quantity.

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

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

Jun 22, 2018

Integral Calculus

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

Jun 21, 2018

Limit

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

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.