Properties of Logarithms definitions Flashcards
Properties of Logarithms definitions
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Logarithmic Expression Mathematical statement involving a logarithm, often manipulated using properties to expand or condense its form. Product Rule Property allowing the log of a product to be written as the sum of the logs of its factors. Quotient Rule Property allowing the log of a quotient to be written as the difference of the logs of numerator and denominator. Power Rule Property allowing an exponent inside a log to be moved in front as a multiplier. Expansion Process of rewriting a single log expression as a sum or difference of multiple logs using log properties. Condensation Process of combining multiple log terms into a single log expression by applying log properties in reverse. Base Number that serves as the reference for the logarithm, found as the subscript in log notation. Change of Base Formula Method for rewriting a log in terms of logs with a different base, often to simplify calculation. Common Logarithm Logarithm with base 10, typically written as 'log' and available as a calculator function. Natural Logarithm Logarithm with base e, written as 'ln', commonly used in mathematics and available on calculators. Exponent Number indicating how many times a base is multiplied by itself, often manipulated using the power rule in logs. Calculator Evaluation Process of using a calculator to compute the value of a log, often after changing its base to 10 or e. Single Log Logarithmic expression condensed into one term, often the result of applying condensation. Multiple Logs Expanded form of a log expression, consisting of several log terms connected by addition or subtraction. Logarithmic Base e Special base for logs, denoted as e (approximately 2.718), used in natural logarithms.