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.

June 18, 2018

Algebra Trigonometry

Find $x^3+\dfrac{1}{x^3}$ if value of $x+\dfrac{1}{x}$ equals to $2\cos{θ}$

Jun 13, 2018

Limit

Learn how to solve Limit of (1-cos6x)/(1-cos7x) as $x$ approaches $0$

Jun 09, 2018

Trigonometry

Find ΣtanAtanB, if A+B+C = 90°

May 30, 2018

Trigonometry

Find cos 40° + cos 80° + cos 160°

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.