Editing Logarithm (section)

==Motivation==
[[File:Binary logarithm plot with grid.png|right|thumb|upright=1.35|alt=Graph showing a logarithmic curve, crossing the ''x''-axis at ''x''= 1 and approaching minus infinity along the ''y''-axis.|The [[graph of a function|graph]] of the logarithm base 2 crosses the [[x axis|''x''-axis]] at {{math|''x'' {{=}} 1}} and passes through the points {{nowrap|(2, 1)}}, {{nowrap|(4, 2)}}, and {{nowrap|(8, 3)}}, depicting, e.g., {{math|log<sub>2</sub>(8) {{=}} 3}} and {{math|2<sup>3</sup> {{=}} 8}}. The graph gets arbitrarily close to the {{mvar|y}}-axis, but [[asymptotic|does not meet it]].]]
[[Addition]], [[multiplication]], and [[exponentiation]] are three of the most fundamental arithmetic operations. The inverse of addition is [[subtraction]], and the inverse of multiplication is [[division (mathematics)|division]]. Similarly, a logarithm is the inverse operation of [[exponentiation]]. Exponentiation is when a number {{mvar|b}}, the ''base'', is raised to a certain power {{mvar|y}}, the ''exponent'', to give a value {{mvar|x}}; this is denoted
<math display="block">b^y=x.</math>
For example, raising {{math|2}} to the power of {{math|3}} gives {{math|8}}: <math>2^3 = 8.</math>

The logarithm of base {{mvar|b}} is the inverse operation, that provides the output {{mvar|y}} from the input {{mvar|x}}. That is, <math>y = \log_b x</math> is equivalent to <math>x=b^y</math> if {{mvar|b}} is a positive [[real number]]. (If {{mvar|b}} is not a positive real number, both exponentiation and logarithm can be defined but may take several values, which makes definitions much more complicated.)

One of the main historical motivations of introducing logarithms is the formula 
<math display="block">\log_b(xy)=\log_b x + \log_b y,</math>
by which [[logarithm table|tables of logarithms]] allow multiplication and division to be reduced to addition and subtraction, a great aid to calculations before the invention of computers.