At constant temperature for adsorption of a gas on a solid, the plot of $\text{log}$ $\left(\frac{x}{m}\right)$ vs $\text{log P}$ is linear with slope equal to:
(Where, $x,m,P$ represent their usual meaning, $k$ is a constant and n being a whole number)

The correct option is D $\frac{1}{n}$
According to freundlich adsorption isotherm, for adsorption of a gas on a solid, the extent of adsortion $\left(\frac{x}{m}\right)$ varies with $P$ as given below:
$\left(\frac{x}{m}\right)$= $k(P{)}^{\frac{1}{n}}$
Where $k$ is constant.
Taking log on either side
$\text{log}\left(\frac{x}{m}\right)=\text{log}k+\frac{1}{n}\text{log}P$
It is analogous to $\text{y=c + mx}$ which is equation of a straight line.

$\therefore$ Plot of $\log \left(\frac{x}{m}\right)\text{vs}\log P$ is linear with a slope of $\frac{1}{n}$.