The expression you've provided is \(-\log\left(p^4\right)\).

To simplify this, we'll again use the logarithm power rule, which states:

\[
\log(a^b) = b \cdot \log(a)
\]

Applying this rule to your expression:

\[
-\log\left(p^4\right) = - \left(4 \cdot \log(p)\right)
\]

This simplifies to:

\[
-4 \cdot \log(p)
\]

So, the simplified form of the expression is:

\[
-4\log(p)
\]

Would you like to explore any additional details or have further questions?

Here are 8 related questions for deeper understanding:
1. How do you simplify \( \log(a^b \times c^d) \)?
2. What happens when you take the logarithm of a negative number?
3. How does the logarithm of a product relate to the logarithms of its factors?
4. What are the differences between natural logarithms and common logarithms?
5. How can logarithmic identities help in solving complex logarithmic equations?
6. How do you simplify expressions like \( \log\left(\frac{a}{b}\right) \)?
7. What is the inverse function of a logarithm?
8. How can logarithms be used to determine the growth rate in exponential models?

**Tip:** Remember that the logarithm of a number raised to a power simplifies by bringing the exponent in front as a multiplier. This rule is essential for solving and simplifying logarithmic expressions efficiently.

Learn how to simplify -log(p^4) using the logarithm power rule. This problem involves logarithmic expressions and their simplification, crucial for high school mathematics.

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