Question

explain why the plot of the function n^c is a straight line with slope c on a log-log scale

Answer 1

Answer on Question #63021, Programming & Computer Science / Other

Explain why the plot of the function $n^{\wedge}c$ is a straight line with slope $c$ on a log-log scale.

Answer:

Given a power law equation $y = an^c$, taking the logarithm of the equation (with any base) yields:

$$\log y = c \log n + \log a$$

Setting $X = \log n$ and $Y = \log y$, which corresponds to using a log-log graph, yields the equation of the line:

$$Y = m X + b$$

where $m = c$ is the slope of the line (gradient) and $b = \log a$ is the intercept on the $(\log y)$-axis.

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