# Convert nonlinear regression equation to a linear regression equation

The question is:

"Show how the nonlinear regression equation y=aX^B can be converted to a linear regression equation solvable by the method of least squares."

I found how to take Y=Ae^(bX)u to a linear equation: y=a+bX+v where y=ln(Y);a=ln(A);v=ln(u).

However, I feel like there is a key difference between that example and my equation. The base of the exponential equation is e in their example and X in mine. The base being e in their example is what allows then to simplify ln(e^(bX))=bX... right? So I'm not sure what to do with my equation. I'm assuming the answer is not as simple as y=a+Bln(X).... Because this is still not linear.

Any help explaining this would be greatly appreciated!

If $y = aX^B$ then $\log y = (\log a) + B\log X$. The intercept is $\log a$ and the slope is $B$; the independent and dependent variables are $\log X$ and $\log y$. The base of the logarithms can be any positive number except $1$.