Log–log plot: Difference between revisions

Revision as of 20:54, 24 June 2021

Revision as of 17:23, 2 December 2021

Line 5:

== Relation with monomials ==

Given a monomial equation <math>y=ax^k,</math> taking the logarithm of the equation (with any base) yields:

:<math display="block">\log y = k \log x + \log a.</math>

Setting <math>X = \log x</math> and <math>Y = \log y,</math> which corresponds to using a log–log graph, yields the equation:

:<math display="block">Y = mX + b</math>

where ''m''&nbsp;=&nbsp;''k'' is the slope of the line ([[Grade (slope)|gradient]]) and ''b''&nbsp;=&nbsp;log&nbsp;''a'' is the intercept on the (log&nbsp;''y'')-axis, meaning where log&nbsp;''x''&nbsp;=&nbsp;0, so, reversing the logs, ''a'' is the ''y'' value corresponding to ''x''&nbsp;=&nbsp;1.<ref>[http://www.intmath.com/Exponential-logarithmic-functions/7_Graphs-log-semilog.php M. Bourne ''Graphs on Logarithmic and Semi-Logarithmic Paper'' (www.intmath.com)]</ref>