BackProperties of Logarithms definitions
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1/15BackSkip to main contentBackLogarithm
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.
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