Linearize the equation B = k l rⁿ

The equation to be linearized is:

$$B = k l r^n$$

Using the properties $\ln(xy) = \ln x + \ln y$ and $\ln(x^p) = p \ln x$, expand the right side of the equation:

$$\ln(B) = \ln(k) + \ln(l) + \ln(r^n)$$ $$\ln(B) = \ln(k) + \ln(l) + n \ln(r)$$

If we consider $\ln(B)$ as the dependent variable ($Y$) and $\ln(r)$ as the independent variable ($X$), then $\ln(k) + \ln(l)$ acts as the constant y-intercept ($C$).

$$\ln(B) = n \ln(r) + (\ln(k) + \ln(l))$$

This equation is now in a linear form. If $\ln(B)$ is plotted against $\ln(r)$, a straight line will be obtained with a gradient of $n$ and a y-intercept of $\ln(k) + \ln(l)$.