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.
-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
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
Other uses for“e”
The value "e" is
So now that “e” is known to you, let’s
move on to solving logarithmic equations.
All right, one
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.
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
Use natural logs
to solve the next equation
Now use common
logs to solve the same problem
What do you notice?