To find the elasticity of demand $E(p)$, we need to apply the formula for elasticity in terms of price-demand function:

$E(p) = \frac{p}{x} \cdot \frac{dx}{dp}$

Given: $x = f(p) = 155 - 30 \ln(p)$

Let's proceed step-by-step:

Step 1: Find $\frac{dx}{dp}$

Differentiate $x = 155 - 30 \ln(p)$ with respect to $p$:

$\frac{dx}{dp} = -\frac{30}{p}$

Step 2: Substitute into the elasticity formula

Now we substitute $x = 155 - 30 \ln(p)$ and $\frac{dx}{dp} = -\frac{30}{p}$ into the elasticity formula:

$E(p) = \frac{p}{155 - 30 \ln(p)} \cdot \left(-\frac{30}{p}\right)$

Step 3: Simplify the expression

The $p$ terms cancel out, giving:

$E(p) = \frac{-30}{155 - 30 \ln(p)}$

Thus, the elasticity of demand $E(p)$ is:

$E(p) = \frac{-30}{155 - 30 \ln(p)}$

Would you like further details on this process or have any other questions?

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Here are some related questions you might consider:

1. What is the interpretation of a negative elasticity value?
2. How does the elasticity of demand change as $p$ increases?
3. What does it mean if $E(p) = -1$ at a particular price $p$?
4. How can this elasticity value be used to predict revenue changes with price adjustments?
5. What are the conditions under which this demand function would be considered elastic or inelastic?

Tip: Remember, elasticity greater than 1 (in magnitude) indicates elastic demand, less than 1 indicates inelastic demand, and exactly 1 means unitary elasticity.