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Properties of Logarithms definitions

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  • Logarithm
    A mathematical operation that undoes exponentiation, revealing the exponent needed to reach a value from a given base.
  • Exponential Function
    A function where a constant base is raised to a variable exponent, forming the inverse relationship with logarithms.
  • Inverse Property
    A rule stating that applying a logarithm and an exponential with the same base cancels both, leaving only the exponent or argument.
  • Product Rule
    A property allowing the logarithm of a product to be written as the sum of the logarithms of the factors.
  • Quotient Rule
    A property allowing the logarithm of a quotient to be written as the difference of the logarithms of the numerator and denominator.
  • Power Rule
    A property allowing an exponent inside a logarithm to be moved in front as a multiplier of the logarithm.
  • Change of Base Formula
    A method for rewriting a logarithm in terms of logs with a different base, using a fraction of two logarithms.
  • Common Logarithm
    A logarithm with base 10, often written simply as 'log' and found as a calculator button.
  • Natural Logarithm
    A logarithm with base e, written as 'ln', commonly used in calculus and available on calculators.
  • Expansion
    The process of rewriting a single logarithmic expression as a sum, difference, or multiple of simpler logs.
  • Condensation
    The process of combining multiple logarithmic terms into a single logarithm using log properties in reverse.
  • Base
    The fixed number in a logarithm or exponential that is raised to a power or used as the reference for the log.
  • Argument
    The value inside a logarithm, representing the number for which the exponent is being solved.
  • Exponent
    The power to which a base is raised in an exponential or the result found by evaluating a logarithm.
  • Fractional Exponent
    An exponent expressed as a fraction, often representing roots, such as 1/3 for a cube root.