Introduction:
In a nutshell, the concept behind this lesson is to review and
extend important ideas involving symbolic reasoning with exponential
expressions and equations, as well as to learn about natural logarithms
and how to solve logarithmic equations.
Objectives:
-To understand the number “e” and natural logarithms.
-To solve logarithmic equations involving either common logarithms
or natural logarithms.
Log Functions with Different Bases
So what is the
Natural log?
The man who came up with the number 2.71828182846
was named John Napier, but the man who gave that number the symbol
“e” was named Leonhard Euler. Euler is commonly referred
to as the “inventor” of “e” and he gave
it that symbol when he was trying to work on the problem of continually
compounded interest.
Other uses for“e”
Besides being
used for
problems
involved
in continually
compounded
interest, “e”can
also be
used to
show bacterial
growth.
If the
problem
has the
bacteria
increasing
by 150%
during
a given
unit of
time, values
will ultimately
approach
an asymptote
involving
"e".
The value "e" is
also used
for modeling
simple population
growth, such
as rabbit
offspring
growth, or
half-life
showing exponential
decay.
So now that “e” is known to you, let’s
move on to solving logarithmic equations.
Let’s try
another one...
All right, one
more....
And now here’s
an example of solving a natural log...
So, as you can see, solving natural logarithms is
really no different than solving any other logarithms.
Here’s one
more example of a natural log
This really doesn’t do much for you, however,
because you can press the calculator key, ln4, and get the same
answer.
Use natural logs
to solve the next equation
Now use common
logs to solve the same problem
What do you notice?
