Use the rule logb(xy)=logbx+logby

Question

to find log4(16⋅64)
.(1 point)

Answer 1

To find \( \log_4(16 \cdot 64) \) using the property \( \log_b(xy) = \log_b(x) + \log_b(y) \), we first rewrite the expression:

\[ \log_4(16 \cdot 64) = \log_4(16) + \log_4(64) \]

Next, we need to calculate \( \log_4(16) \) and \( \log_4(64) \).

1. Calculate \( \log_4(16) \): \[ 16 = 4^2 \implies \log_4(16) = 2 \]

2. Calculate \( \log_4(64) \): \[ 64 = 4^3 \implies \log_4(64) = 3 \]

Now, we can add these results together:

\[ \log_4(16 \cdot 64) = \log_4(16) + \log_4(64) = 2 + 3 = 5 \]

Thus, the final answer is:

\[ \log_4(16 \cdot 64) = 5 \]