Answer
A natural logarithmic function.
Work Step by Step
The conversion of polar coordinates and Cartesian coordinates are described as follows:
1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$
2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
3. $x=r \cos \theta$ and 4. $y=r \sin \theta$
Given: $\ln r+\ln \cos \theta=\ln (r \cos \theta)$
Thus, the Cartesian equation is $y=\ln x$
Hence, this shows a natural logarithmic function.
