Use the price-demand equation to find $E(p)$, the elasticity of demand.
$$x=f(p)=165-85\ln (p)$$
$$E(p)=$$

Step 1 ：We are given the price-demand equation $x=f(p)=165-85\ln (p)$, and we are asked to find the elasticity of demand $E(p)$.

Step 2 ：The formula for the elasticity of demand is given by: $E(p)=p\cdot \frac{f^{\prime }(p)}{f(p)}$, where $f^{\prime }(p)$ is the derivative of the price-demand function $f(p)$ with respect to $p$.

Step 3 ：First, we find the derivative of the function $f(p)$. The derivative of $f(p)=165-85\ln (p)$ with respect to $p$ is $f^{\prime }(p)=-85/p$.

Step 4 ：Now that we have the derivative of the function $f(p)$, we can substitute it into the formula for the elasticity of demand $E(p)$.

Step 5 ：Substituting $f^{\prime }(p)=-85/p$ and $f(p)=165-85\ln (p)$ into the formula for $E(p)$, we get $E(p)=p\cdot \frac{-85/p}{165-85\ln (p)}$.

Step 6 ：Simplifying the above expression, we get $E(p)=\frac{-85}{165-85\ln (p)}$.

Step 7 ：$\boxed{{\displaystyle E(p)=\frac{-85}{165-85\ln (p)}}}$ is the final answer.