Stuck on graphing question

• Mar 21st 2009, 05:38 AM
cross1933
Stuck on graphing question
Can someone start me in the right direction for a homework problem. I am using a TI-83 calculator for this class. Here is the problem,
"Solve the equation using a graphing calculator, 2 ln 2 - ln x = -1"
• Mar 21st 2009, 06:51 AM
stapel
Quote:

Originally Posted by cross1933
"Solve the equation using a graphing calculator, 2 ln 2 - ln x = -1"

The "right" way to do this is of course whatever way they showed you in class. (Wink)

But one method would be to graph Y1 = 2*ln(2)-ln(x) and Y2 = -1, and have the graphing calculator find the intersection point of the two lines (with a command something like "ISECT").

Another way would be to notice that 2*ln(2) - ln(x) will equal -1 for the same x-value(s) for which 2*ln(2) - ln(x) + 1 will equal zero. So graph Y1 = 2*ln(2)-ln(x)+1, and have the calculator find the "ROOT" or "zero".

You'll need to check your owners manual, in the chapter on graphing, for the specific commands.

. . . . .Prentice-Hall: Graphing Calculator Help
. . . . .MathBits: Finding Your Way Around...

Have fun! :D
• Mar 21st 2009, 07:55 AM
cross1933
Quote:

Originally Posted by stapel
The "right" way to do this is of course whatever way they showed you in class. (Wink)

But one method would be to graph Y1 = 2*ln(2)-ln(x) and Y2 = -1, and have the graphing calculator find the intersection point of the two lines (with a command something like "ISECT").

Another way would be to notice that 2*ln(2) - ln(x) will equal -1 for the same x-value(s) for which 2*ln(2) - ln(x) + 1 will equal zero. So graph Y1 = 2*ln(2)-ln(x)+1, and have the calculator find the "ROOT" or "zero".

You'll need to check your owners manual, in the chapter on graphing, for the specific commands.

. . . . .Prentice-Hall: Graphing Calculator Help
. . . . .MathBits: Finding Your Way Around...

Have fun! :D

Online course, material not impressive. I have purchase two other books and researched online information.

I used both of your suggested methods,came up with X=2.712 & Y=1.388. I see my way of getting to this point was correct but I am still missing something in the process to obtain the correct final result.
• Mar 21st 2009, 10:08 AM
sinewave85
Quote:

Originally Posted by cross1933
Online course, material not impressive. I have purchase two other books and researched online information.

I used both of your suggested methods,came up with X=2.712 & Y=1.388. I see my way of getting to this point was correct but I am still missing something in the process to obtain the correct final result.

Finding an intersect with a TI83 can be a little tricky. First, you need to make sure that the point where the two functions intersect is on the screen. For this problem, you need to set the viewing window to something like this (stretching the y axis makes it easier to see the point of intersection):
Xmin=2
Xmax=22
Xscl=1
Ymin=-5
Ymax=5
Yscl=1
Then you go to the calc menu and choose "5:intersect." The calculator will ask you for the "first curve", and you need to position the cursor to the left of the point of intersection on Y1 and hit enter. Then it will ask you for the "second curve" and you need to position the cursor to the right of the point of intersection on Y2 (the calculator will automatically switch to the other function) and hit enter. The calculator will display "Guess?" and you need to hit enter again. It will display "Intersection" and give the answer of X = 10.873127, Y= -1. Hope that helps!
• Mar 21st 2009, 10:30 AM
sinewave85
As a side note, if you check the answer by solving the equation for x:

$\displaystyle x = e^{1 + 2\ln(2)} = 10.87312731$

you will note that the answer obtained by using the calc function is less accurate than the answer obtained by solving the equation.
• Mar 21st 2009, 10:51 AM
cross1933
Quote:

Originally Posted by sinewave85
Finding an intersect with a TI83 can be a little tricky. First, you need to make sure that the point where the two functions intersect is on the screen. For this problem, you need to set the viewing window to something like this (stretching the y axis makes it easier to see the point of intersection):
Xmin=2
Xmax=22
Xscl=1
Ymin=-5
Ymax=5
Yscl=1
Then you go to the calc menu and choose "5:intersect." The calculator will ask you for the "first curve", and you need to position the cursor to the left of the point of intersection on Y1 and hit enter. Then it will ask you for the "second curve" and you need to position the cursor to the right of the point of intersection on Y2 (the calculator will automatically switch to the other function) and hit enter. The calculator will display "Guess?" and you need to hit enter again. It will display "Intersection" and give the answer of X = 10.873127, Y= -1. Hope that helps!

My problem was a operational error. The steps you provided helped to clear up my issue.
Thanks