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

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: \[ \log v \]