https://file.aiquickdraw.com/mathbot/file/1738343617209km68ezzn.jpg

Let's solve the equation:

\[
\log 8x - \log 2 = \log 32
\]

Step-by-step:

1. **Apply the logarithmic rule** \( \log a - \log b = \log \left(\frac{a}{b}\right) \):
   \[
   \log \left(\frac{8x}{2}\right) = \log 32
   \]
   This simplifies to:
   \[
   \log (4x) = \log 32
   \]

2. **Since the logarithms are equal**, we can drop the log and equate the inside of the logarithms:
   \[
   4x = 32
   \]

3. **Solve for \( x \)**:
   \[
   x = \frac{32}{4} = 8
   \]

Thus, the solution is \( x = 8 \).

### Answer: \( x = 8 \) (This matches one of the choices in the image you uploaded).

Would you like further explanation or help with similar problems? Here's some related practice to deepen your understanding:

1. How do you handle equations involving logarithms with different bases?
2. What if the equation involved \( \log x + \log y \) instead of subtraction?
3. Can you explain the logarithmic identity \( \log a^b = b \log a \)?
4. How can you verify the solution to a logarithmic equation?
5. What’s the domain of a logarithmic function?

**Tip:** Always remember to check that the argument of a logarithm is positive, as the logarithm of a non-positive number is undefined.

Learn how to solve the logarithmic equation log 8x - log 2 = log 32 using logarithmic properties. This step-by-step solution applies key concepts such as the quotient rule of logarithms and equality property of logarithms. Suitable for students in Grades 9-12.

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