Use properties of logarithms to evaluate the expression. Assume all expressions exist and are well-defined. \( \log _{v} v^{14}-\log _{v} v^{9} \) Submit

Let's apply the properties of logarithms to evaluate the expression \( \log _{v} v^{14}-\log _{v} v^{9} \). Using the property that states \( \log_{b} a - \log_{b} c = \log_{b} \left(\frac{a}{c}\right) \), we can combine the logs: \[ \log_{v} v^{14} - \log_{v} v^{9} = \log_{v} \left(\frac{v^{14}}{v^{9}}\right) \] Next, we simplify the fraction: \[ \frac{v^{14}}{v^{9}} = v^{14-9} = v^{5} \] So, we have: \[ \log_{v} (v^{5}) \] Now applying the property that states \( \log_{b} (b^{k}) = k \), we get: \[ \log_{v} (v^{5}) = 5 \] Therefore, the final answer is \( 5 \).