Given the relation y = axⁿ, how do you find the constants a and n using logarithms?

To find the constants $a$ and $n$ from the relation $y = ax^n$, we first linearize the equation by taking the logarithm of both sides. Using $\log_{10}$:

Step 1: Linearize the equation.

$$y = ax^n$$ $$\log_{10} y = \log_{10} (ax^n)$$ $$\log_{10} y = \log_{10} a + \log_{10} (x^n)$$ $$\log_{10} y = n \log_{10} x + \log_{10} a$$

This equation is in the form $Y = mX + C$, where $Y = \log_{10} y$, $X =