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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 1.8 : Logarithm Functions
Without using a calculator determine the exact value of each of the following.
- \({\log _7}343\)
- \({\log _4}1024\)
- \(\displaystyle {\log _{\frac{3}{8}}}\frac{{27}}{{512}}\)
- \(\displaystyle {\log _{11}}\frac{1}{{121}}\)
- \({\log _{0.1}}0.0001\)
- \({\log _{16}}4\)
- \(\log 10000\)
- \(\ln \frac{1}{{\sqrt[5]{{\bf{e}}}}}\)
Write each of the following in terms of simpler logarithms
- \({\log _7}\left( {10{a^7}{b^3}{c^{ - 8}}} \right)\)
- \(\log \left[ {{z^2}{{\left( {{x^2} + 4} \right)}^3}} \right]\)
- \(\displaystyle \ln \left( {\frac{{{w^2}\,\sqrt[4]{{{t^3}}}}}{{\sqrt {t + w} }}} \right)\)
Combine each of the following into a single logarithm with a coefficient of one.
- \(7\ln t - 6\ln s + 5\ln w\)
- \(\displaystyle \frac{1}{2}\log \left( {z + 1} \right) - 2\log x - 4\log y - 3\log z\)
- \(\displaystyle 2{\log _3}\left( {x + y} \right) + 6{\log _3}x - \frac{1}{3}\)
Use the change of base formula and a calculator to find the value of each of the following.
- \({\log _7}100\)
- \(\displaystyle {\log _{\frac{5}{7}}}\frac{1}{8}\)