1)) Use properties of logarithms to evaluate the expression. Assume all expressions exist and are well-defined. $$ \log v^{3}+\log v^{4}-\log v^{6} $$

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To evaluate the expression $$ \log v^{3} + \log v^{4} - \log v^{6} $$, we can use the properties of logarithms. Here are the steps:

1. **Use the Product Property of Logarithms**: The property states that $$ \log a + \log b = \log(ab) $$. We can apply this to the first two terms:
   $$
   \log v^{3} + \log v^{4} = \log(v^{3} \cdot v^{4})
   $$

2. **Combine the Exponents**: When multiplying powers with the same base, we add the exponents:
   $$
   v^{3} \cdot v^{4} = v^{3+4} = v^{7}
   $$
   So, we have:
   $$
   \log(v^{3} \cdot v^{4}) = \log(v^{7})
   $$

3. **Use the Quotient Property of Logarithms**: The property states that $$ \log a - \log b = \log\left(\frac{a}{b}\right) $$. We can apply this to the result from step 2 and the third term:
   $$
   \log(v^{7}) - \log(v^{6}) = \log\left(\frac{v^{7}}{v^{6}}\right)
   $$

4. **Simplify the Fraction**: When dividing powers with the same base, we subtract the exponents:
   $$
   \frac{v^{7}}{v^{6}} = v^{7-6} = v^{1} = v
   $$
   Thus, we have:
   $$
   \log\left(\frac{v^{7}}{v^{6}}\right) = \log(v)
   $$

Putting it all together, the evaluated expression is:
$$
\log v
$$
The expression simplifies to $$ \log v $$.

1)) Use properties of logarithms to evaluate the expression. Assume all expressions exist and are well-defined. \( \log v^{3}+\log v^{4}-\log v^{6} \)

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