To determine the value of \(\log_4 16\), we need to figure out to what power we must raise 4 to get 16.
We begin by setting up the expression:
[tex]\[ \log_4 16 = x \][/tex]
This can be rewritten in exponential form as:
[tex]\[ 4^x = 16 \][/tex]
Next, we need to recall that 16 is a power of 4. Specifically, we can express 16 as:
[tex]\[ 16 = 4^2 \][/tex]
So, we substitute this back into our equation:
[tex]\[ 4^x = 4^2 \][/tex]
Since the bases are the same, we can equate the exponents:
[tex]\[ x = 2 \][/tex]
Thus, the value of [tex]\(\log_4 16\)[/tex] is [tex]\(\boxed{2}\)[/tex].
