To solve the equation \( x = \log_4 8 \), we need to express \( x \) in a way that is more easily solvable.

### Step 1: Express the logarithm in terms of a more familiar base
We know that:
\[
\log_a b = \frac{\log_c b}{\log_c a}
\]
where \( c \) is any positive number. A common choice for \( c \) is 10 (common logarithm) or \( e \) (natural logarithm), but for simplicity, we will use base 2 because both 4 and 8 are powers of 2.

### Step 2: Rewrite \( \log_4 8 \) in terms of base 2
First, express 4 and 8 as powers of 2:
\[
4 = 2^2 \quad \text{and} \quad 8 = 2^3
\]
Then, substitute these into the logarithm:
\[
\log_4 8 = \log_{2^2} 2^3
\]
Using the change of base formula, we get:
\[
\log_{2^2} 2^3 = \frac{\log_2 2^3}{\log_2 2^2}
\]

### Step 3: Simplify the expression
We know that:
\[
\log_2 2^3 = 3 \quad \text{and} \quad \log_2 2^2 = 2
\]
So:
\[
\log_4 8 = \frac{3}{2}
\]

### Final Answer:
\[
x = \frac{3}{2}
\]

Would you like more details or have any questions?

Here are five related questions for further exploration:

1. How would you solve \( x = \log_5 25 \)?
2. What is \( \log_2 32 \)?
3. How do you convert between logarithms of different bases?
4. Can you solve \( x = \log_4 16 \)?
5. What is the value of \( \log_4 64 \)?

**Tip:** When dealing with logarithms, expressing the numbers in terms of the same base often simplifies the calculation significantly.

Learn how to solve the logarithmic equation x = log4 8 using the change of base formula and basic exponent properties. This detailed step-by-step guide explains key concepts such as expressing logarithms with a common base and simplifying the result. Suitable for students in Grades 9-12.

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