= Log-log plot
{wiki=Log–log_plot}
A <log-log plot> uses <logarithmic scales> on both axes. For a positive <power law> $y=Cx^p$ with $x,C>0$, positive references $x_0,y_0$ give
$$
\log_b(y/y_0)=\log_b(Cx_0^p/y_0)+p\log_b(x/x_0).
$$
Its transformed <slope> is the exponent $p$ when both axes use the same <logarithm> base and the <slope> is measured in logarithmic coordinate units. For example, $y=2x^2$ takes the values $2,8,32$ at $x=1,2,4$. Every doubling of $x$ quadruples $y$, giving <slope> two on a <log-log plot>.
This differs from a <semi-log plot>: a <power law> has constant proportional response to a proportional change of input, whereas <exponential growth> has constant proportional response to an additive change of input. Both can appear straight with appropriate axes, so one must read the scale labels before interpreting a <slope>.
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