To input `e^(2x)+e^x-6=0` in a TI-84 calculator:
There are a couple of different ways. The most straight forward:
(1) Hit the Y= button
(2) Clear any equations showing (Hit CLEAR button)
(3) The first line should show `\Y_1=` -- key in `e^(2x)+e^x-6`
** The `e^x` button is above the LN button -- hit 2nd LN **
**For `e^(2x)` , when you hit 2nd LN the calculator displays e^( , just put in 2X (Use the `X,T,theta,n` button for x) **
(4) Now hit the GRAPH button, and the function should graph.
You are looking for the zero -- the point where the graph crosses the y-axis.
(5) Hit calc (2nd TRACE) then 2 (zero)
The calculator will return to the graph with a blinking cursor. In the lower left corner the calculator will ask for the lower bound -- you can either enter a number or use the arrow keys to locate any point to the left of the zero. I would just hit 0; enter.
The calculator now asks for a right bound. Again you can enter a number or use the arrow keys to move the cursor anywhere to the right of the zero. I entered 1.
The calculator now asks for a guess. You can select any number between your endpoints, including the endpoints. You can also use the arrow keys to move the cursor close to the zero. (This sometimes helps speed up the search). I entered 1.
In the lower left corner, the calculator should display the approximate zero. In this case it returns `x~~.69314718` . Calculators can make mistakes, so checking the answer you get:
`e^(1.38629436)+e^.69314718-6~~-5.5995x10^(-9)=0` for all practical purposes.
Thus the answer you will get, to two decimal places, is `x~~.69`