To solve the equation \( \log_{1/16} (x) = \frac{1}{4} \), let's proceed step by step:

### Step 1: Understand the logarithmic equation
The equation \( \log_{1/16} (x) = \frac{1}{4} \) means:
\[
x = (1/16)^{1/4}
\]

### Step 2: Simplify the expression \( (1/16)^{1/4} \)
First, express \( 1/16 \) as a power of 2:
\[
1/16 = \frac{1}{2^4} = 2^{-4}
\]

Now, calculate \( (2^{-4})^{1/4} \):
\[
(2^{-4})^{1/4} = 2^{-4 \times \frac{1}{4}} = 2^{-1} = \frac{1}{2}
\]

### Final Answer:
\[
x = \frac{1}{2}
\]

So, the solution to the equation \( \log_{1/16} (x) = \frac{1}{4} \) is \( x = \frac{1}{2} \).

Would you like more details on this solution or have any questions? 

Here are some related questions:

1. How do you convert logarithmic equations to exponential form?
2. Why is the logarithm of a number with a base less than 1 negative?
3. What is the significance of the base in a logarithmic equation?
4. How do you simplify fractional exponents?
5. Can logarithmic equations have more than one solution?
6. What happens if the base of the logarithm is negative?
7. How do you solve logarithmic equations with variable bases?
8. What are some real-world applications of logarithms?

**Tip:** When dealing with logarithmic equations, it's helpful to convert the logarithm into its exponential form. This often simplifies the problem, making it easier to solve.

Learn how to solve the logarithmic equation log base 1/16 of x equals 1/4 step-by-step. This problem involves logarithmic concepts and exponential equations. Suitable for students in Grades 10-12.

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