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Let's solve the given expression step by step:

The expression is:
\[
\log(35) - \log(5) + \log\left(\frac{7}{8}\right)
\]

### Step 1: Use the logarithmic subtraction property
\[
\log(a) - \log(b) = \log\left(\frac{a}{b}\right)
\]
Applying this to the first two terms:
\[
\log(35) - \log(5) = \log\left(\frac{35}{5}\right) = \log(7)
\]

### Step 2: Use the logarithmic addition property
\[
\log(a) + \log(b) = \log(ab)
\]
Now add the remaining term:
\[
\log(7) + \log\left(\frac{7}{8}\right) = \log\left(7 \times \frac{7}{8}\right) = \log\left(\frac{49}{8}\right)
\]

### Final Expression
The simplified expression is:
\[
\log\left(\frac{49}{8}\right)
\]

Looking at the answer choices, we see that this corresponds to option **D**:
\[
\log(7^2) + \log(8) = \log\left(\frac{49}{8}\right)
\]

Would you like more details or have any further questions?

Here are five related questions to explore this topic further:
1. How does the property \(\log(a) - \log(b) = \log\left(\frac{a}{b}\right)\) work in general?
2. Can you simplify \(\log\left(\frac{x}{y}\right)\) using logarithmic properties?
3. What happens when you apply the power rule \(\log(a^b) = b\log(a)\)?
4. How would you solve similar problems with natural logarithms \(\ln\) instead of common logarithms \(\log\)?
5. Can the logarithmic properties be applied to non-real numbers?

**Tip:** Always remember that the logarithmic rules can simplify complex expressions, but they must be applied correctly in the right order to avoid mistakes.

Simplify the following: log(35) - log(5) + log(7/8).

This problem simplifies a logarithmic expression using logarithmic properties. It involves concepts like log subtraction and addition, making it suitable for students in grades 9-12. Learn how to break down and solve log expressions step by step.

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