1. By : Daniel Carter

2.  A logarithm is 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 ln x is the inverse of the real exponential function e x.

4.  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.  The exponential function with positive base b > 1 is the function  y = b x.  It is defined for every real number x. Here is its graph:

7.  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.