1. ## root of equation

hello how would i show that the equation $\displaystyle lnx = 4-x$ has one real root..

am not sure what to do with the $\displaystyle lnx$ function

2. You want the zeros of $\displaystyle f(x) = \ln x + x -4$, $\displaystyle 0<x<+\infty$. Observe by differentiation that f is strictly increasing. Therefore if f has at most one root, since if a<b were two distinct roots we could chuse a<c<b, and 0=f(a)<f(c)<f(b)=0, a contradiction. To see that one root exists, evaluate f near zero to get a negative value and then above 4 to get a positive value and use the IVT.

3. Hello, sigma1!

How would i show that the equation $\displaystyle \ln x \:=\: 4-x$ has one real root?

Graph the functions: .$\displaystyle \begin{Bmatrix}y &=& \ln x \\ y &=& 4-x \end{Bmatrix}$ . and note their intersection(s), if any.
Code:
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* |
4o
| *                     *
|   *            *
|     *     *
|       ◊
|    *    *
- - + -o- - - - o - - - - - - - - - -
| *1        4  *
|                 *
|*
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