# Thread: How to solve this simple exponential equation?

1. ## How to solve this simple exponential equation?

(16e^x) - (16e^2x) = 3

2. Rewrite it as $\displaystyle 0 = 16e^{2x} - 16e^x + 3$

$\displaystyle 0 = 16\left(e^x\right)^2 - 16e^x + 3$.

Now let $\displaystyle X = e^x$ so that the equation becomes

$\displaystyle 0 = 16X^2 - 16X + 3$, which is a quadratic equation you can solve for $\displaystyle X$, and then solve for $\displaystyle x$.

3. Originally Posted by Yehia
(16e^x) - (16e^2x) = 3 and the answer says that x = 0.25 but i can't see how you can get there? please help, much appreciated!! thanks!

Have you correctly quoted the problem?

4. Originally Posted by Prove It
Rewrite it as $\displaystyle 0 = 16e^{2x} - 16e^x + 3$

$\displaystyle 0 = 16\left(e^x\right)^2 - 16e^x + 3$.

Now let $\displaystyle X = e^x$ so that the equation becomes

$\displaystyle 0 = 16X^2 - 16X + 3$, which is a quadratic equation you can solve for $\displaystyle X$, and then solve for $\displaystyle x$.
thanks

5. Originally Posted by Yehia
(16e^x) - (16e^2x) = 3 and the answer says that x = 0.25 but i can't see how you can get there? please help, much appreciated!! thanks!

Thank you very much for answering to my previous question. Please, post your work if you get some of this

(i) $x=0,25$ is a solution of the given equation.

(ii) The equation has only one solution.