For the function f(x)=4x

Question

, the value when x=3
is f(3)=43=64
. What is log464
?

Answer 1

To find \( \log_4{64} \), we can express 64 as a power of 4:

\[ 64 = 4^3 \]

Next, we can use the property of logarithms:

\[ \log_b{(a^c)} = c \cdot \log_b{a} \]

Applying this property, we have:

\[ \log_4{64} = \log_4{(4^3)} = 3 \cdot \log_4{4} \]

Since \( \log_4{4} = 1 \), we can simplify this to:

\[ \log_4{64} = 3 \cdot 1 = 3 \]

Thus, the value of \( \log_4{64} \) is

\[ \boxed{3} \]