Solving+for+a+variable+in+the+exponent

Algebra - Request or Give Help

Given that 9^2x-1 = 3^3x + 3, what value of x satisfies the equation?

Notes:**
 * Solution by Tim Fahlberg: [|Mathcast]
 * 1) From experience I assumed that the equation was : 9^(2x-1) = 3^(3x + 3) . If this assumption is incorrect please let us know. I assumed this based on experience with solving similar problems.
 * 2) I solved this problem by using a purely algebraic approach. Could someone else solve this using a graphical approach perhaps using the TI virtual calculator or new TI-SmartView?
 * 3) In this solution I catch an error I had made at the end when I checked the answer I had worked out. Then I found and fixed the error. I left the error in rather than re-doing the movie for two reasons: 1) I think it's important that others see the mistakes we make and how we catch them and 2) I didn't want to re-do the movie. Let's face it - Who has time to try to make perfect movies? I don't and I encourage you to be happy with less than perfect movies. No one expects you to be perfect in real life so why should it be any different with mathcasts unless they really have to be perfect for some non-educational purpose?

Personally, even if I were the young student, I believe I would be forced to admit "Algebra is the best approach for many situations." After viewing Tim's mathcast and then viewing this "calculator approach" to finding a solution, I want to have the algebraic knowledge and only use the calculator as a means of checking and verifying, NOT as a primary means of finding a solution.
 * Another View by Robert Fant:** [|**Using TI-SmartView**]

On the other hand, maybe someone can show us an even better way to use the calculator. Perhaps someone will make a mathcast demonstrating the calculators "equation solving" capabilities.


 * Feedback from cmk7**

Leaving out the parentheses (unintentionally) provided more information than expected. When we start getting hundreds of math questions each week, there will likely be many problems that are open to interpretation. Until a better solution is found, perhaps a mathcast that shows students how to type in common math symbols would be useful.

I like that fact that the movie wasn't edited. We make mistakes in the classroom with our students so it is more realistic to show those same types of mistakes in our mathcasts. More importantly, the error was discovered during the checking process which reinforces how important that step is.


 * Feedback from Tim Fahlberg**

You're so right! We need a simple way for people to type in common math symbols. Apparently the Wikispaces people are currently working on adding this feature but until then I would like to offer the following method for doing this. I'll describe it and then follow this up with a screencast showing the steps ([|here's the screencast]). And if you can think of a simpler way to do this please let us know!

Adding common math symbols > Notes: >> >>
 * 1) Using SMART Notebook software (free, version 9.5 has math equation editing) + Microsoft Paint (free)
 * 1) Open up a SMART Notebook.
 * 2) Type or use graphics tablet to write a math equation or math expression with symbols.
 * 3) Resize equation as desired.
 * 4) Select and copy equation.
 * 5) Open up Microsoft Paint (Start - Programs - Accessories).
 * 6) Paste equation.
 * 7) Resize box to fit equation.
 * 8) Save equation as a .png image file.
 * 9) Add this image to the desired page using the //Add Image// tool.
 * 1) These steps are actually quite easy to do and take very little time.
 * 2) If you try to Export a SMART Notebook as images you'll get one image per page and each image will be quite large even if only a small portion of a page actually has something on it.
 * 3) I tried using Microsoft Paint all by itself and "writing" and equation with a mouse but it gave unsatisfactory results.

Algebra - Request or Give Help