To evaluate [tex]\( \log_4 256 \)[/tex], we need to determine the power to which the base 4 must be raised to obtain 256.
The expression [tex]\( \log_b(a) = c \)[/tex] means that [tex]\( b^c = a \)[/tex]. Therefore:
[tex]\[ \log_4(256) = x \][/tex]
implies
[tex]\[ 4^x = 256 \][/tex]
Next, we should recognize if 256 can be expressed as a power of 4. We proceed by determining the power relationship here:
[tex]\[
4^1 = 4 \\
4^2 = 16 \\
4^3 = 64 \\
4^4 = 256
\][/tex]
We see that:
[tex]\[ 256 = 4^4 \][/tex]
Therefore:
[tex]\[ 4^4 = 256 \][/tex]
This means:
[tex]\[ \log_4(256) = 4 \][/tex]
Thus, the correct answer is:
A. 4
