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: \(E(p) = p \cdot \frac{f'(p)}{f(p)}\), where \(f'(p)\) 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 \(f'(p) = -85/p\).

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 \(f'(p) = -85/p\) 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 ：\(\boxed{E(p) = \frac{-85}{165 - 85 \ln (p)}}\) is the final answer.