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 viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 6.2 : Logarithm Functions
11. Without using a calculator determine the exact value of \(\ln {{\bf{e}}^4}\).
Show All Steps Hide All Steps
Hint : Recall that converting a logarithm to exponential form can often help to evaluate these kinds of logarithms. Also recall what the base is for a natural logarithm.
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.