To solve the equation \( \log_4 2 = 3x - 8 \), we'll break it down into simple steps:

### Step 1: Understand the logarithmic expression
The equation \( \log_4 2 \) represents the logarithm of 2 with base 4. This asks, "To what power must 4 be raised to get 2?"

### Step 2: Solve the logarithm
Since \( 4^{\frac{1}{2}} = 2 \), we know that:
\[
\log_4 2 = \frac{1}{2}
\]
So the equation becomes:
\[
\frac{1}{2} = 3x - 8
\]

### Step 3: Solve for \( x \)
Now, solve the linear equation \( \frac{1}{2} = 3x - 8 \).

1. **Add 8 to both sides** to isolate the term with \( x \):
   \[
   \frac{1}{2} + 8 = 3x
   \]
   \[
   \frac{1}{2} + \frac{16}{2} = 3x
   \]
   \[
   \frac{17}{2} = 3x
   \]

2. **Divide both sides by 3** to solve for \( x \):
   \[
   x = \frac{\frac{17}{2}}{3}
   \]
   \[
   x = \frac{17}{6}
   \]

### Final Answer
The solution is:
\[
x = \frac{17}{6} \approx 2.83
\]

Would you like any more details or have any questions?

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**Related Questions:**
1. What are the properties of logarithms and how can they be used in equations?
2. How do you solve logarithmic equations with different bases?
3. Can logarithms with a base greater than the number ever be negative?
4. How does the change of base formula work in logarithms?
5. What are some real-world applications of logarithms?

**Tip:** Remember, logarithms are the inverse operations of exponentiation. This can help simplify complex logarithmic problems.

Learn how to solve the logarithmic equation log base 4 of 2 equals 3x minus 8 step-by-step. This problem involves logarithmic concepts and linear equations. Suitable for students in Grades 10-12.

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