Joshua Psalms T. answered • 05/12/16

Tutor

5
(5)
Civil EIT, Former College Professor of Mathematics (in Asia)

An example of that is this:

Solve for:

e

^{2x}- 4e^{x}+ 3 = 0;You can actually manipulate the power but it would be like this: (we know that (b

^{m})^{n}= b^{mn}right?)So we can rewrite the equation as:

(e

^{x})^{2}- 4e^{x}+ 3 = 0Now, we let the e

^{x}= m (or any other variable that you like except x) and it will be:m

^{2}- 4m + 3 = 0Voila, your quadratic equation. By factoring:

(m-3)(m-1) = 0

m - 3 = 0 m - 1 = 0

m = 3 m = 1

Return the value of 'm':

e

^{x}= 3 e^{x}= 1**x = ln3**

**x = ln1 = 0**

***The actual equation given here is y = e**

^{2x}- 4e^{x}+ 3. But since solving for x also means solving for the "zeroes" of an equation, these are actually the x-intercepts. Meaning, you will let y = 0 and proceed on the process above.*