91Ó°ÊÓ

For the following exercise, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as asum, difference, or product of logs. $$ \log \left(\sqrt{x^{3} y^{-4}}\right) $$

For the following exercise, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as asum, difference, or product of logs. $$ \ln \left(y \sqrt[4]{\frac{y}{1-v}}\right) $$

For the following exercise, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as asum, difference, or product of logs. $$ \log \left(x^{2} y^{3} \sqrt[3]{x^{2} y^{5}}\right) $$

For the following exercises, condense each expression to a single logaritim using the properties of logaritims. $$ \log \left(2 x^{4}\right)+\log \left(3 x^{5}\right) $$

For the following exercises, condense each expression to a single logaritim using the properties of logaritims. $$ \ln \left(6 x^{9}\right)-\ln \left(3 x^{2}\right) $$

For the following exercises, condense each expression to a single logaritim using the properties of logaritims. $$ 2 \log (x)+3 \log (x+1) $$

For the following exercises, condense each expression to a single logaritim using the properties of logaritims. $$ \log (x)-\frac{1}{2} \log (y)+3 \log (z) $$

For the following exercises, condense each expression to a single logaritim using the properties of logaritims. $$ 4 \log _{7}(c)+\frac{\log _{7}(a)}{3}+\frac{\log _{7}(b)}{3} $$

For the following exercises, rewrite each expression as an equivalent ratio of logs using the indicated base. $$ \log _{7}(15) \text { to base } e $$

For the following exercises, rewrite each expression as an equivalent ratio of logs using the indicated base. $$ \log _{14}(55.875) \text { to base } 10 $$