Introduction to Logarithms definitions Flashcards
Introduction to Logarithms definitions
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Logarithm Inverse operation to exponentiation, providing the power a base must be raised to in order to yield a specific number. Exponential Equation Mathematical statement where the variable appears in the exponent, such as 2^x = 8. Logarithmic Form Expression written as log base b of m equals x, representing the exponent needed for b to yield m. Exponential Form Expression written as b to the power of x equals m, showing a base raised to an exponent. Base Number that is repeatedly multiplied in exponentiation or used as the reference in a logarithm. Common Logarithm Logarithm with base 10, often written simply as 'log' and commonly found on calculators. Natural Logarithm Logarithm with base e, denoted as 'ln', frequently used in mathematics and science. Inverse Property Rule stating that a logarithm and an exponential with the same base cancel, leaving only the exponent or argument. Exponent Number indicating how many times a base is multiplied by itself in an exponential expression. Cube Root Value that, when multiplied by itself three times, yields the original number; used to reverse cubing. Logarithmic Equation Equation involving a logarithm, often used to solve for exponents in exponential equations. Logarithmic Property Characteristic or rule that simplifies or evaluates logarithmic expressions, such as log base b of b equals 1. Equivalent Statement Two mathematical expressions, such as exponential and logarithmic forms, that represent the same relationship. Calculator Notation Special symbols or buttons, like 'log' for base 10 and 'ln' for base e, used for evaluating logarithms. Exponent Rule Guideline for manipulating exponents, such as converting roots to fractional exponents for use in logarithms.
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