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##### Logarithms

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**Logarithms**By : Daniel Carter**What is logarithm**• Alogarithmis a number to a given base is the power or exponent to which the base must be raised in order to produce that number. • Only positive real numbers have real number logarithms; negative and complex numbers have complex logarithms. • A complex logarithm is a function is an "inverse" of the complex exponential function, just as the natural logarithm lnx is the inverse of the real exponential function ex.**Two vocabulary words**• Base-the power or exponent to which the base must be raised in order to produce that number • hyperbolic geometry-is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced.**Example**• The exponential function with positive base b > 1 is the function • y = bx. • It is defined for every real number x. Here is its graph:**Where can I used logarithms in the real world**• You can use logarithms in a earthquake. The scale that is used to measure earthquakes, the Richter Scale, involves a logarithm. Likewise the scale that is used to measure the loudness of sound in decibles involves a logarithm. They are often used in studying population growth and radioactive decay.