Answer
A natural logarithmic function.
Work Step by Step
Conversion of polar coordinates and Cartesian coordinates are as follows:
a)$r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$
b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
c) $x=r \cos \theta$
d) $y=r \sin \theta$
Here, we have $\ln r+\ln \cos \theta=\ln (r \cos \theta)$
Therefore, our Cartesian equation is $y=\ln x$
This shows a natural logarithmic function.
