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1. Logarithms By : Daniel Carter

2. 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.

3. Picture

4. 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.

5. 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:

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7. 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.