Condense each expression to a single logarithm. \( \begin{array}{ll}\text { 13) } \log 3-\log 8 & \text { 14) } \frac{\log 6}{3} \\ \text { 15) } 4 \log 3-4 \log 8 & \text { 16) } \log 2+\log 11+\log 7 \\ \text { 17) } \log _{7} 7-2 \log 12 & \text { 18) } \frac{2 \log 7}{3} \\ \begin{array}{ll}\text { 19) } 6 \log _{3} u+6 \log _{3} v & \text { 20) } \ln x-4 \ln y \\ \text { 21) } \log _{4} u-6 \log _{4} v & \text { 22) } \log _{3} u-5 \log _{3} v \\ \text { 23) } 20 \log _{6} u+5 \log _{6} v & \text { 24) } 4 \log _{3} u-20 \log _{3} v\end{array}\end{array} . \begin{array}{l}\text { (1) }\end{array} \)

Certainly! Below are the condensed forms of each logarithmic expression reduced to a single logarithm: --- **13) \(\log 3 - \log 8\)** Using the quotient rule: \[ \log \left(\frac{3}{8}\right) \] --- **14) \(\frac{\log 6}{3}\)** Using the power rule: \[ \log \left(6^{\frac{1}{3}}\right) \quad \text{or} \quad \log \sqrt[3]{6} \] --- **15) \(4 \log 3 - 4 \log 8\)** Factor out the 4 and apply the quotient rule: \[ 4 \left(\log 3 - \log 8\right) = \log \left(\left(\frac{3}{8}\right)^4\right) \] --- **16) \(\log 2 + \log 11 + \log 7\)** Using the product rule: \[ \log (2 \times 11 \times 7) = \log 154 \] --- **17) \(\log_{7} 7 - 2 \log_{7} 12\)** Simplify and apply the quotient rule: \[ \log_{7} 7 - \log_{7} (12^2) = \log_{7} \left(\frac{7}{144}\right) \] --- **18) \(\frac{2 \log 7}{3}\)** Using the power and then the root: \[ \log \left(7^{\frac{2}{3}}\right) \quad \text{or} \quad \log \sqrt[3]{7^2} \] --- **19) \(6 \log_{3} u + 6 \log_{3} v\)** Factor out the 6 and apply the product rule: \[ 6 (\log_{3} u + \log_{3} v) = \log_{3} (u \times v)^6 = \log_{3} (u^6 v^6) \] --- **20) \(\ln x - 4 \ln y\)** Using the quotient rule: \[ \ln \left(\frac{x}{y^4}\right) \] --- **21) \(\log_{4} u - 6 \log_{4} v\)** Using the quotient rule: \[ \log_{4} \left(\frac{u}{v^6}\right) \] --- **22) \(\log_{3} u - 5 \log_{3} v\)** Using the quotient rule: \[ \log_{3} \left(\frac{u}{v^5}\right) \] --- **23) \(20 \log_{6} u + 5 \log_{6} v\)** Using the product rule: \[ 20 \log_{6} u + 5 \log_{6} v = \log_{6} (u^{20} \times v^5) = \log_{6} (u^{20} v^5) \] --- **24) \(4 \log_{3} u - 20 \log_{3} v\)** Using the quotient rule: \[ 4 \log_{3} u - 20 \log_{3} v = \log_{3} \left(\frac{u^4}{v^{20}}\right) \] --- These condensed forms utilize the fundamental logarithmic identities: the product rule (\(\log a + \log b = \log(ab)\)), the quotient rule (\(\log a - \log b = \log(a/b)\)), and the power rule (\(k \log a = \log(a^k)\)) to combine multiple logarithmic terms into a single logarithm.