The properties of logarithms in this section can be used to rewrite log2⁡𝑥5 as follows:𝐴⁢log2⁡𝐵Find the values for 𝐴 and 𝐵:

To rewrite $\log_2(x^5)$ using properties of logarithms, we need to apply the power rule of logarithms, which states:

$\log_b(a^n) = n \cdot \log_b(a)$

Step 1: Break Down the Problem

We need to express $\log_2(x^5)$ in the form $A \cdot \log_2(B)$.

Step 2: Relevant Concepts

Using the power rule:

1. Identify $n$: In this case, $n = 5$.
2. Identify $a$: Here, $a = x$.
3. Identify $b$: The base $b = 2$.

Step 3: Analysis and Detail

Applying the power rule:

$\log_2(x^5) = 5 \cdot \log_2(x)$

From this expression, we can see that:

• $A = 5$
• $B = x$

Step 4: Verify and Summarize

We verified that we applied the logarithmic property correctly. Therefore, we summarize the values:

Final Answer

The values are $A = 5$ and $B = x$.