Calculus I - Logarithm Functions (Assignment Problems)

Show Mobile Notice Show All Notes Hide All Notes

Mobile Notice

You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Assignment Problems Notice

Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.

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.

\({\log _7}100\)
\(\displaystyle {\log _{\frac{5}{7}}}\frac{1}{8}\)