Can you use non-linear variables in a linear regression model?

Let us assume a function such as $y = k {x}^{a}$, where $k$ and $a$ are two constants.
By taking logs of both sides, we get $\log y = \log k + a \log x$, which can be written as $\overline{y} = \overline{k} + a \overline{x}$, a linear relation between $\overline{y} = \log y$ and $\overline{x} = \log x$.