Question

Use the rule logb(xy)=logbx+logby
to find log2(16⋅64)
.(1 point)

Answer 1

To use the rule \( \log_b(xy) = \log_b x + \log_b y \) to find \( \log_2(16 \cdot 64) \), we can break it down as follows:

1. **Calculate \( \log_2 16 \)**:
- We know that \( 16 = 2^4 \), so:
\[
\log_2 16 = \log_2 (2^4) = 4
\]

2. **Calculate \( \log_2 64 \)**:
- We also know that \( 64 = 2^6 \), so:
\[
\log_2 64 = \log_2 (2^6) = 6
\]

3. **Apply the rule**:
- Now, using the rule:
\[
\log_2(16 \cdot 64) = \log_2 16 + \log_2 64
\]
- Substitute the values we found:
\[
\log_2(16 \cdot 64) = 4 + 6 = 10
\]

Thus, \( \log_2(16 \cdot 64) = 10 \).