The expression you've provided is \( \log\left(p^{\frac{1}{2}}\right) \).

You can simplify this logarithmic expression using the logarithm power rule, which states:

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

Applying this rule to the expression:

\[
\log\left(p^{\frac{1}{2}}\right) = \frac{1}{2} \cdot \log(p)
\]

So, the simplified form of the expression is:

\[
\frac{1}{2} \log(p)
\]

Would you like to go over any additional details or have any questions?

Here are 8 related questions you might find interesting:
1. How do you simplify \( \log(a \times b) \)?
2. What is the value of \( \log(1) \) and why?
3. How do you apply logarithms to solve exponential equations?
4. What are the properties of logarithms that are most commonly used in algebra?
5. Can you explain the change of base formula for logarithms?
6. How do you solve logarithmic equations involving different bases?
7. What does it mean when a logarithm has a negative result?
8. How do you use logarithms in real-world applications, such as in finance or physics?

**Tip:** When working with logarithms, remember that the base of the logarithm is crucial. If the base isn't specified, it's typically assumed to be 10 (common logarithm) or \(e\) (natural logarithm).

Learn how to simplify the logarithmic expression \( \log(p^{1/2}) \) using the logarithm power rule. Understand the step-by-step process and applications in algebra and calculus. Suitable for Grades 10-12.

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