Editing Logarithm (section)

===Graph of the logarithm function===
[[File:Logarithm inversefunctiontoexp.svg|right|thumb|The graph of the logarithm function {{math|log<sub>''b''</sub>&thinsp;(''x'')}} (blue) is obtained by [[Reflection (mathematics)|reflecting]] the graph of the function {{math|''b''<sup>''x''</sup>}} (red) at the diagonal line ({{math|1=''x'' = {{mvar|y}}}}).|alt=The graphs of two functions.]]
As discussed above, the function {{math|log<sub>''b''</sub>}} is the inverse to the exponential function <math>x\mapsto b^x</math>. Therefore, their [[graph of a function|graphs]] correspond to each other upon exchanging the {{mvar|x}}- and the {{mvar|y}}-coordinates (or upon reflection at the diagonal line {{Math|1=''x'' = ''y''}}), as shown at the right: a point {{math|1=(''t'', ''u'' = {{mvar|b}}<sup>''t''</sup>)}} on the graph of {{Mvar|f}} yields a point {{math|1=(''u'', ''t'' = log<sub>''b''</sub>&thinsp;''u'')}} on the graph of the logarithm and vice versa. As a consequence, {{math|log<sub>''b''</sub>&thinsp;(''x'')}} [[divergent sequence|diverges to infinity]] (gets bigger than any given number) if {{mvar|x}} grows to infinity, provided that {{mvar|b}} is greater than one. In that case, {{math|log<sub>''b''</sub>(''x'')}}  is an [[increasing function]]. For {{math|''b'' < 1}}, {{math|log<sub>''b''</sub>&thinsp;(''x'')}} tends to minus infinity instead. When {{mvar|x}} approaches zero, {{math|log<sub>''b''</sub>&thinsp;''x''}} goes to minus infinity for {{math|''b'' > 1}} (plus infinity for {{math|''b'' < 1}}, respectively).