Use the rule logb(xy)=logbx+logby

Question

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