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
11. Without using a calculator determine the exact value of \(\ln {{\bf{e}}^4}\).
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Recalling that the base for a natural logarithm is \(\bf{e}\) and converting the logarithm to exponential form gives,
\[\ln {{\bf{e}}^4} = {\log _{\bf{e}}}{{\bf{e}}^4} = ?\hspace{0.25in} \Rightarrow \hspace{0.25in}{{\bf{e}}^?} = {{\bf{e}}^4}\] Show Step 2From this we can quickly see that \({{\bf{e}}^4} = {{\bf{e}}^4}\) and so we must have,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{\ln {{\bf{e}}^4} = 4}}\]Note that an easier method of determining the value of this logarithm would have been to recall the properties of logarithm. In particular the property that states,
\[{\log _b}{b^x} = x\]Using this we can also very quickly see what the value of the logarithm is.