I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 6.2 : Logarithm Functions
10. Without using a calculator determine the exact value of \({\log _{\frac{1}{4}}}16\).
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Converting the logarithm to exponential form gives,
\[{\log _{\frac{1}{4}}}16 = ?\hspace{0.25in} \Rightarrow \hspace{0.25in}{\left( {\frac{1}{4}} \right)^?} = 16\] Show Step 2Now, we know that if we raise an fraction to a power and get an integer out we must have had a negative exponent. Now, we also know that \({4^2} = 16\). Therefore, we can see that \({\left( {\frac{1}{4}} \right)^{ - 2}} = {\left( {\frac{4}{1}} \right)^2} = 16\) and so we must have,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{{{\log }_{\frac{1}{4}}}16 = - 2}}\]