In this video, I will show how to use
Desmos.com to graph and create a table of values
for each log function shown here.
We'll notice how, for the first log function,
we have common log, or log base 10.
For the second log function, we have natural log,
or log base e.
And for the third function, we have log base two.
We don't have to use the change of base formula
when using Desmos.com.
We can enter a log function of any base.
The first step is to go to Desmos.com
and click Start Graphing.
And now we enter the first log function,
which is y equals log open parenthesis x minus two
closed parenthesis minus four, enter.
Notice how we have the graph on the right.
We can adjust the window by click-and-dragging
on the coordinate plane.
If we click on the wrench here,
we can click Projector Mode,
which makes the graph much thicker and easier to read.
We can also adjust the window manually here.
Let's close this menu by clicking outside the menu.
If we click on the graph and scroll,
we can see approximate ordered pairs
for points on the graph.
But let's also create a table of values.
To do this, we go to the left, click on the plus,
select Table.
We need to change y sub one to the log expression
log of the quantity x minus two minus four,
but we do have to use the variable x sub one.
So let's clear y sub one,
enter log open parenthesis,
to get x sub one, we can just press x1,
and then minus two, closed parenthesis, minus four, enter.
And now we need to enter the x-values for the table.
Notice the domain is when x is greater than two.
So let's start x sub one at two, enter, three, enter,
and now we can simply keep pressing enter
to get more rows in the table.
Notice how the function value's undefined when x is two,
because two is not in the domain.
Notice how the corresponding points
are graphed on the function.
If we click on the points, we can see the ordered pairs.
And now we have plenty of information to make a nice graph
of this first log function.
And now let's graph the second log function.
Let's go ahead and clear these
by clicking on the X's on the right,
and the second log function is y equals
negative natural log, open parenthesis, x,
closed parenthesis, plus one.
Let's click-and-drag on the coordinate plane
to adjust the window.
If we click to the right of the equation here,
notice how the horizontal intercept
is already graphed for us.
If we scroll over the point, we can see the ordered pair.
And if we click on the function and drag,
we can see approximate ordered pairs
for points on the graph.
Let's create a table of values
by clicking the plus sign, selecting Table.
Let's go up to y sub one, clear this,
and we'll enter negative natural log
open parenthesis, x1, closed parenthesis, plus one, enter.
Notice the domain is when x is greater than zero.
Let's start x sub one at zero,
which gives us an undefined function value.
Enter, one, enter, enter, enter, enter, and so on,
which gives us points on the graph.
If for some reason we wanted to change
the color of the points or the color of the graph,
to change the color of the points
we can click and hold on this button,
and select a different color, let's say red.
If we wanted to change the color of the function,
we can click here and hold,
and select a different color, let's say black.
If we click on the points on the graph,
again we will see the ordered pairs,
which gives us plenty of information
to make a nice graph of the function.
If we did want a function value, let's say x is 0.5,
we can go back to the table and enter 0.5,
and it will give us the corresponding function value.
Now let's go ahead and graph our last function,
which has a logarithm with base two.
So let's clear these.
Go up to y1, enter y equals three.
To enter log base two, we enter log,
and to get to the base position,
we need to press Shift + Minus.
Again, Shift + Minus takes us to the position of the base.
We enter two, right arrow takes out of the base position,
we enter open parenthesis x plus one,
closed parenthesis, and then minus two, enter.
Another way to adjust the window
is to click the plus or minus,
which is zoom in and zoom out.
If we zoom out, and then click-and-drag
on the coordinate plane, we can get
a nice view of the graph.
If we click to the right of the equation,
notice how the vertical and horizontal intercepts
are already graphed for us.
If we click-and-drag on the function,
we can see ordered pairs.
Let's create a table of values.
Click plus, select Table,
clear y1, we enter three,
L-O-G, Shift + Minus takes us to the position of the base,
we enter two, right arrow, open parenthesis x1
plus one, closed parenthesis, minus two, enter.
Notice the domain is when x is greater than negative one.
Let's start the table at negative one, enter,
zero, enter, one, enter, and then keep pressing enter
to get more ordered pairs.
And if we click on the points,
we can see the specific ordered pairs.
Okay, hope you found this helpful.