The problem requires evaluating $\log_4(16)$.

Solution:

The expression $\log_4(16)$ means "to what power must 4 be raised to get 16?"

1. Write the logarithmic equation as an exponential equation: $4^x = 16$

2. Rewrite 16 as a power of 4: $4^x = 4^2$

3. Since the bases are the same, equate the exponents: $x = 2$

Final Answer:

$\log_4(16) = 2$

Let me know if you'd like further clarification or additional examples.

Here are 5 related questions to deepen your understanding:

1. Evaluate $\log_3(27)$.
2. Solve $\log_5(125)$.
3. Simplify $\log_2(8)$.
4. If $\log_b(81) = 4$, find $b$.
5. Convert $\log_7(49)$ to exponential form and solve.

Tip:

Remember, logarithms are the inverse of exponentials. Always try rewriting the equation in exponential form to solve quickly!