What is the value of ${\log }_{4}16$?

• A. $8$
• B. $4$
• C. $2$
• D. $\frac{1}{2}$

Answer: (C)

Verified step by step guidance

1. Understand that the expression \( \log_4 16 \) asks: "To what power must 4 be raised to get 16?"
2. Recall that 16 can be expressed as a power of 4. Since \( 4^2 = 16 \), rewrite 16 as \( 4^2 \).
3. Use the logarithm property: \( \log_b (b^k) = k \), where \( b \) is the base and \( k \) is the exponent.
4. Apply this property to \( \log_4 16 = \log_4 (4^2) \), which simplifies to 2.
5. Therefore, the value of \( \log_4 16 \) is the exponent 2, because 4 raised to the power 2 equals 16.