https://file.aiquickdraw.com/mathbot/file/1727023707990ywznff0d.jpg

The extracted text from the image isn't clear. However, based on visual inspection, the expression appears to be:

\[
\log 2 + \log 3 - \log 6 - \log 8
\]

Let's proceed by simplifying this expression.

### Step-by-step simplification:

1. Use the logarithmic identity:
   \[
   \log a + \log b = \log(ab)
   \]
   and
   \[
   \log a - \log b = \log\left(\frac{a}{b}\right)
   \]
   Apply this identity to combine the terms:
   \[
   (\log 2 + \log 3) - (\log 6 + \log 8)
   \]
   becomes:
   \[
   \log(2 \times 3) - \log(6 \times 8)
   \]

2. Simplify the products:
   \[
   \log 6 - \log 48
   \]

3. Apply the subtraction identity:
   \[
   \log\left(\frac{6}{48}\right)
   \]

4. Simplify the fraction:
   \[
   \log\left(\frac{1}{8}\right)
   \]

5. Using the logarithmic property for reciprocals:
   \[
   \log\left(\frac{1}{8}\right) = -\log 8
   \]

Thus, the simplified expression is:
\[
-\log 8
\]

Would you like more details on any specific steps, or do you have any questions? 

### Related questions:
1. What is the general rule for combining logarithms?
2. How does the reciprocal rule of logarithms work?
3. Can logarithmic expressions involving division be simplified further?
4. How would you solve logarithmic equations like this involving different bases?
5. What is the role of the natural logarithm \(\ln\) in simplifying log expressions?

### Tip:
Remember to always apply logarithmic rules step-by-step, as each one transforms the expression into a simpler form.

Learn how to simplify the logarithmic expression log 2 + log 3 - log 6 - log 8 with a detailed step-by-step solution. This problem involves logarithmic identities such as the product and quotient rules, suitable for students in Grades 10-12.

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