LOGARITHMS

• A logarithm is the exponent to which a base is raised to obtain a given value. 
• A logarithmic function is the inverse of the exponential function. 
• A logarithm base 10 is called a common logarithm. Logarithms with no base are assumed to be base ten. Example log 5 is a common logarithm

Application of Logarithms: Richter Scale

Logarithms have many applications in science and engineering. One of such applications is in the Richter scale, the device pictured above used in measuring the magnitude of earthquakes. Charles Richter in 1935 defined the magnitude of an earthquake to be \(M = \log \frac{I}{S}\) where I is the intensity of the earthquake and S is the intensity of a standard earthquake and M i the magnitude of a standard earthquake.