For the function f(x)=4x

Question

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

Answer 1

To find \( \log_4 64 \), we can start by expressing 64 as a power of 4.

We know that:

\[ 64 = 4^3 \]

This is because:

\[ 4^1 = 4 \] \[ 4^2 = 16 \] \[ 4^3 = 64 \]

Now, using the definition of logarithms, we have:

\[ \log_4 64 = \log_4 (4^3) \]

By the properties of logarithms, we can simplify this to:

\[ \log_4 (4^3) = 3 \]

Thus, the value of \( \log_4 64 \) is:

\[ \log_4 64 = 3 \]