Chapter 8

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log 45 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{3} 81 $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2} x y^{3}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln \frac{1}{2} $$

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log 75 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{2} 16 $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2}(x \div y)\)

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log 27 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{3} 81 \cdot \log _{2} 16 $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2}\left(x^{2} \div y^{3}\right)\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln \frac{1}{36} $$

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log \frac{1}{3} $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{5} 125 $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2} \sqrt{x y}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln \frac{2}{3} $$

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log \frac{1}{5} $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{10} 1,000 $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2} x \sqrt{y}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln \left(\frac{2}{3}\right)^{2} $$

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log 0.04 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{2} 32 $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2} \frac{\sqrt{x}}{y^{3}}\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln a^{2} $$

In \(36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log \frac{9}{10} $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2} \sqrt{\frac{x}{y}}\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln a^{3} $$

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log \frac{3}{5} $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{3} 81 $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2} x \sqrt{x}\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln a^{-1} $$

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log \left(\frac{3}{5}\right)^{2} $$

Write each expression in terms of \(A\) and \(B\) if \(\log _{2} x=A\) and \(\log _{2} y=B\). \(\log _{2} \sqrt[4]{y}\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln \frac{1}{a} $$

In \(48-55,\) if \(\log a=c,\) express each of the following in terms of \(c\) $$ \log a^{2} $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{6} 36 $$

Solve each equation for the variable. \(\log _{2} 2^{3}+\log _{2} 2^{2}=\log _{2} x\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln a^{-2} $$

In \(48-55,\) if \(\log a=c,\) express each of the following in terms of \(c\) $$ \log 10 a $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{\frac{1}{3}} 27 $$

Solve each equation for the variable. \(\log _{2} 16+\log _{2} 2=\log _{2} x\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln \frac{1}{a^{2}} $$

In \(48-55,\) if \(\log a=c,\) express each of the following in terms of \(c\) $$ \log 100 a $$

Solve each equation for the variable. \(\log _{2} x-\log _{2} 8=\log _{2} 4\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln a^{\frac{1}{2}} $$

In \(48-55,\) if \(\log a=c,\) express each of the following in terms of \(c\) $$ \log \frac{a}{10} $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{5} 125 \cdot \log _{10} 1,000 \cdot 2 \log _{2} 32 $$

Solve each equation for the variable. \(\log _{5} x+\log _{5} x=\log _{5} 625\)

In \(45-52,\) if \(\ln a=c,\) express each of the following in terms of \(c\) $$ \ln \sqrt{a} $$

In \(48-55,\) if \(\log a=c,\) express each of the following in terms of \(c\) $$ \log \frac{100}{a} $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{\frac{1}{2}} \frac{1}{4} \cdot \log _{3} 81 \cdot \frac{1}{2} \log _{18} 324 $$