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Properties of Logarithms definitions

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  • Product Rule
    Allows the log of a product to be written as the sum of separate logs with the same base.
  • Quotient Rule
    Enables the log of a quotient to be expressed as the difference between two logs with the same base.
  • Power Rule
    Permits an exponent inside a log to be moved in front as a multiplier of the log.
  • Expansion
    Process of rewriting a single log expression as a sum or difference of multiple logs using log properties.
  • Condensation
    Combining multiple log terms into a single log expression by applying log properties in reverse.
  • Base
    The number that serves as the foundation for the logarithmic operation, indicated as a subscript.
  • Common Logarithm
    A logarithm with base 10, often written simply as 'log' and used frequently in calculations.
  • Natural Logarithm
    A logarithm with base e, denoted as 'ln', commonly used in mathematics and science.
  • Change of Base Formula
    A method for rewriting a log in terms of logs with a different base, using a ratio of two logs.
  • Exponent
    A value indicating how many times a base is multiplied by itself, often manipulated using the power rule.
  • Logarithmic Expression
    A mathematical statement involving a log, which can be expanded or condensed using log properties.
  • Simplification
    The process of reducing a log expression to its most basic or compact form using log rules.
  • Calculator Evaluation
    The use of a calculator to compute the value of a log, often after changing its base to 10 or e.
  • Logarithmic Base
    The subscript value in a log that determines the number raised to a power to yield the argument.
  • Argument
    The value inside a log function, representing the number for which the log is being calculated.