We want to graph the following
logarithmic functions using desmos.com.
We have y equals log of x.
Notice how here there is no base given,
and therefore, we know this is
common log, the log base 10.
And then we have y equals natural log x.
Natural log x is log base e.
Number three, we have y
equals log base six of x.
And number four, we have y
equals log base 1/2 of x.
The nice thing about using desmos.com
is we don't normally have to use
the change of base
formula shown here below.
We can enter a logarithm of any base.
The only exception of this
was I did have an issue
entering the base here of 1/2.
Let's begin by going to desmos.com.
Once on desmos.com, and
click start graphing.
Then we enter the functions on the left.
Our first function is y
equals common log of x.
We enter y equals log, and
then, in parentheses x.
The parentheses are optional,
but I do like to include them.
And then enter, and the
graph appears on the right.
If we want to, we can
click, hold, and drag
to reposition the coordinate
plane to get a better view.
We can also click on the wrench
in the upper right hand corner.
If we click projector mode,
the thickness of the graph changes.
We can also adjust the axes manually here.
Let's click out of this window.
And now, click in cell two
and enter the next function,
which is y equals natural log x.
We enter y equals L-N, and
then, in parentheses x.
Enter.
And again, the graph appears.
Next, we have y equals log base six of x.
We enter y equals log.
To enter the base of six, we
need to press underscore six.
For underscore, we press shift dash,
which is to the right of the zero.
And then, we enter the base of six.
Right arrow to get out
of the base position.
Then we enter the x in parentheses.
And enter.
And again, the graph appears.
And now, the last log function
was the one I had an issue with.
For y equals log base 1/2 of x,
I tried y equals log
underscore one divided by two.
We can see that didn't work.
Next thing I tried to do
was try to enter underscore,
and then, 1/2 in parentheses.
And this is what happened,
which of course is not correct.
So finally, I converted 1/2
to a decimal, which is 0.5.
So I went back and entered underscore 0.5.
That worked, and then,
pressed right arrow,
and then x in parentheses.
And I finally did get the graph,
but the problem with that is
if we had a fraction like 1/3,
we would have to round
1/3 to approximately 0.33
or something similar to that,
and therefore, the graph
would not be 100% accurate.
So, in the base of the log is a fraction,
it might be better to use
the change of base formula,
which, for example, for this log function,
if we press enter, y
equals log base 1/2 of x
is equivalence to y equals natural log x
divided by natural log 1/2,
which can be entered without any issues.
Then we can see the red graph
and the black graph are the same.
I hope you found this helpful.
