https://file.aiquickdraw.com/mathbot/file/17260706840968o3opu0b.jpg

The equation in the image is:

\[
\frac{x}{14} = \log_{128} 8
\]

### Steps to solve for \( x \):

1. **Calculate the logarithm:**
   \[
   \log_{128} 8
   \]
   We can rewrite this logarithmic expression using the change of base formula or by expressing 128 and 8 as powers of 2. 

   \[
   128 = 2^7 \quad \text{and} \quad 8 = 2^3
   \]
   Thus, we have:
   \[
   \log_{128} 8 = \log_{2^7} 2^3
   \]
   Using the property of logarithms, \( \log_{a^b} c^d = \frac{d}{b} \), this becomes:
   \[
   \log_{2^7} 2^3 = \frac{3}{7}
   \]

2. **Substitute the value of the logarithm into the original equation:**

   \[
   \frac{x}{14} = \frac{3}{7}
   \]

3. **Solve for \( x \):**
   Multiply both sides by 14:
   \[
   x = 14 \times \frac{3}{7} = 2 \times 3 = 6
   \]

### Final Answer:
\[
x = 6
\]

Do you need further details on the solution? Here are some related questions:

1. How can we use the change of base formula to calculate logarithms?
2. What are the properties of logarithms and how are they applied?
3. How can logarithms with different bases be simplified using powers of 2?
4. Can this problem be generalized for other values of \( x \) or logarithms?
5. What are common mistakes when working with logarithmic equations?

**Tip:** Understanding how to express numbers as powers of a common base simplifies logarithmic calculations significantly.

Solve the logarithmic equation (x / 14) = log_128 (8) step by step using the properties of logarithms. Learn how to express numbers as powers of 2 and simplify logarithmic expressions.

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