Natural Logarithmic Functions are relatively similar to the Logarithmic Functions we have already learned so far in the unit, the only difference would be the use of an irrational constant known as e.
Like pi, the constant e is a never ending value, therefore is only approximated by the numbers 2.7182…
This value of e is often used as the base of a Logarithmic function in order to find values for matters such as exponential growth/decay and compound interest.
Since a Natural Logarithmic Function has e as its base, the only change we see from what we already know about Logarithmic Functions would be:
Since mathematicians are lazy efficient, the Natural Logarithmic Function above can be simply written as:
The rules we learned about Logarithmic Functions so far all apply to the Natural Logarithmic Functions as well.
That means compressing the following Natural Logarithmic Function:
Would result in the following:
The same can be done for expanding, solving, and verifying...
Graphing 
and 
...
Again, this would be similar to what we have already done. The graphs would look as the graphs of 
and 
would, but will be a bit more horizontally compressed due to the added decimals of its approximate value 2.7182...
Other Stuff:
With the help of a calculator we can verify the following the equations below are true:
and 
Examples:
Oh, yeah... here's a picture of a cat doing math!
Thanks Ryan. Nice touch with the cat doing math!
ReplyDelete