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We are given the equation \( 8^5 = x \) and need to find the equivalent logarithmic form from the provided options.

### Step-by-step:
The general rule for converting an exponential equation \( a^b = c \) into logarithmic form is:
\[
\log_a(c) = b
\]
Here, the base is \( 8 \), the exponent is \( 5 \), and the result is \( x \). Using the formula, we get:
\[
\log_8(x) = 5
\]

Now, let's look for the matching equation in the options:

- **Option (a):** \( \log_x(8) = 5 \) (Not correct; the base and argument are switched)
- **Option (b):** \( \log_5(x) = 8 \) (Not correct; wrong base and argument)
- **Option (c):** \( \log_5(8) = x \) (Not correct; wrong base)
- **Option (d):** \( \log_8(x) = 5 \) (Correct; matches our equation)
- **Option (e):** \( \log_5(5) = x \) (Not correct; wrong base and argument)
- **Option (f):** \( \log_x(5) = 8 \) (Not correct; wrong base and argument)

### Correct answer: **(d) \(\log_8(x) = 5\)**

Would you like more details or further clarification?

### Related Questions:
1. How do you convert logarithmic equations to exponential form?
2. What is the difference between a logarithmic and an exponential equation?
3. How do you evaluate logarithms without a calculator?
4. How can we use logarithmic properties to simplify equations?
5. What are some real-world applications of logarithmic functions?

### Tip:
Always remember that the base of the logarithm corresponds to the base of the exponent when converting between exponential and logarithmic forms.

Learn how to convert the exponential equation 8^5 = x into its logarithmic form. This problem involves understanding the relationship between logarithms and exponential equations. Detailed solution provided for high school math students.

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