The logarithm of a number, properties of logarithms

Definition: the Logarithm of a positive number base called exponent, which need to build to get .

Examples: as ;

because

Logarithm

The natural logarithm

Definition of a logarithm

Examples:

The properties and formula of logarithms

  1. The logarithm of a unit on any basis is zero

  2. The logarithm of the compositions of positive integers is equal to the sum of the logarithms of the multipliers

  3. The logarithm of the share of positive numbers equals the difference of logarithms of dividend and divisor

  4. The logarithm of the degree of positive numbers is equal to the product of the exponent on the logarithm of the base of this degree

The generalized formula of logarithms

The formula of transition from one base of logarithm to another

The implications of the formula of transition from one base of logarithm to another

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