Chapter 8

Write each expression as a single logarithm. 4 \(\log _{2}(x+2)\)

In \(21-32,\) for each given logarithm, find \(x,\) the antilogarithm. Write the answer to four decimal places. $$ \ln x=4.8200 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=1.7790 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{8} 8 $$

Write each expression as a single logarithm. \(\log _{10} y-2 \log _{10}(y-1)\)

In \(21-32,\) for each given logarithm, find \(x,\) the antilogarithm. Write the answer to four decimal places. $$ \ln x=-0.5373 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=2.2030 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ 5 \log _{8} 8 $$

Write each expression as a single logarithm. \(\log _{e} x+2 \log _{e} y-2 \log _{e} z\)

In \(21-32,\) for each given logarithm, find \(x,\) the antilogarithm. Write the answer to four decimal places. $$ \ln x=-0.05729 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=2.5619 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{6} 216 $$

Write each expression as a single logarithm. \(\frac{1}{2} \log _{3} x^{10}-\frac{2}{5} \log _{3} x^{5}\)

In \(21-32,\) for each given logarithm, find \(x,\) the antilogarithm. Write the answer to four decimal places. $$ \ln x=-1.1544 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=4.8200 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ 4 \log _{6} 216 $$

Expand each expression using the properties of logarithms. \(\log _{2} 2 a b\)

In \(21-32,\) for each given logarithm, find \(x,\) the antilogarithm. Write the answer to four decimal places. $$ \ln x=-1 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=-0.5373 $$

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

Expand each expression using the properties of logarithms. \(\log _{3} \frac{10}{x}\)

In \(21-32,\) for each given logarithm, find \(x,\) the antilogarithm. Write the answer to four decimal places. $$ \ln x=-2 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=-0.05729 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ 8 \log _{\frac{1}{2}} 2 $$

Expand each expression using the properties of logarithms. \(\log _{5} a^{-5}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln 6 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=-1.1544 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{4} \frac{1}{16} $$

Expand each expression using the properties of logarithms. \(\log _{10}(x+1)^{2}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln 9 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=-3 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ 3 \log _{4} \frac{1}{16} $$

Expand each expression using the properties of logarithms. \(\log _{4} \frac{x^{6}}{y^{5}}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln 4 $$

In \(24-35,\) for each given logarithm, find the antilogarithm, \(x .\) Write the answer to four decimal places. $$ \log x=-4 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{3} 729 $$

Expand each expression using the properties of logarithms. \(\log _{e} \sqrt{x}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln 12 $$

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log 15 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \frac{1}{3} \log _{3} 729 $$

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

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln 24 $$

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

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ \log _{4} \frac{1}{64} $$

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

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

\(\operatorname{In} 36-47,\) if \(\log 3=x\) and \(\log 5=y,\) write each of the logs in terms of \(x\) and \(y\) $$ \log 25 $$

In \(27-56,\) evaluate each logarithmic expression. Show all work. $$ 16 \log _{4} \frac{1}{64} $$

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 \(y\) $$ \ln \frac{1}{3} $$