Least Square Method to fit into an exponential function

Question

I have some x and y data, and I need to fit those data to $y = \alpha xe^{\beta x}$, using linear least squares regression. If it was $y = \alpha e^{\beta x}$, I could take the natural logarithm of both sides, and solve it like it is $y=mx+b$. But in this question when I do that the result is $$\ln y=\ln \alpha+\ln x+\beta x.$$ which is not linear. The question wants us to solve it specifically with linear least squares regression. What can I do?

Answer 1

My attempt:

$$ ln y = ln \alpha + ln x + \beta x $$ $$ ln \frac{y}{x} = ln \alpha + \beta x $$

where $$Z= ln \frac{y}{x} , \beta_0= ln \alpha \quad and \quad \beta_1 = \beta $$

then, we can write the expression like: $$Z = \beta_0 + \beta_1 x$$