Simplify the expression \( \frac{\log_{4} x}{2} \) for \( x = 16 \).
Apply the change of base formula.
Using the change of base formula, we have \( \log_{4} x = \frac{\log_{e} x}{\log_{e} 4} \). For \( x = 16 \), this becomes \( \log_{4} 16 = \frac{\log_{e} 16}{\log_{e} 4} \).
Calculate \( \log_{4} 16 \).
Since \( 16 = 4^2 \), we find that \( \log_{4} 16 = 2 \). Therefore, \( \frac{\log_{4} 16}{2} = \frac{2}{2} = 1 \).
The simplified expression is \( \boxed{1} \).
Verify the result by substituting \( x = 16 \) back into the original expression.
Substitute \( x = 16 \) into \( \frac{\log_{4} x}{2} \).
We substitute to get \( \frac{\log_{4} 16}{2} \).
Calculate \( \log_{4} 16 \) again.
As previously calculated, \( \log_{4} 16 = 2 \), thus \( \frac{2}{2} = 1 \).
The verification confirms the result is \( \boxed{1} \).
The simplified expression for \( \frac{\log_{4} 16}{2} \) is \( \boxed{1} \). The verification also confirms that the result is \( \boxed{1} \).
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