# Logarithms

The logarithm of a number is the *exponent* which another number, called the *base*,
must be raised to produce that number. An example of this is the logarithm of 100 to base 10 is 2,
which is expressed as $ log_{10}(100) = 2 $, because $10^2=100$. The base, 10, must be raised by
a power of 2 to product 100, $ 10\times10 = 100$. If $ x = b^y $,
then y is the logarithm of $ x $ to base $ b $, and is written as $ y = log_{b}(x) $

Logarithms have many applications in science and engineering, the most common use of it that you see in your day to day life is the use of the decibel unit to measure the sound level. This is a logarithmic scale where an increment of one in the decibel value is equivalent to jump in magnitude, since (very simply) $dB = log_{10}{(SoundLevel)}$.