# Math Help - Equation with 2 solutions

1. ## Equation with 2 solutions

i got this (7(plus minus)sqrt(7^2-4*e*12))/2e now i replaced e with 2.718 because that is the value of e and I got 1.591 and 0.984. Is this hat I what's suppose to do?

Roots are:
x1=ln(3)
x2=ln(4)

3. ## Re: Equation with 2 solutions

Originally Posted by MaxJasper
Roots are:
x1=ln(3)
x2=ln(4)
How did you get that?

4. ## Re: Equation with 2 solutions

Let u=e^x then

u^2-7u+12=0

solve for u then plug into u=e^x and find x.

5. ## Re: Equation with 2 solutions

This is what I got when I solved for u:

U= (loge^x(-12)-2)/-7

The log is base e^x

Am I right?

6. ## Re: Equation with 2 solutions

Hello, RD33!

$\text{Solve for }x\!:\;\;e^{2x}-7e^x+12\:=\:0$

Factor: . $(e^x - 3)(e^x - 4) \:=\:0$

Then: . $\begin{Bmatrix}e^x-3 \:=\:0 & \Rightarrow & e^x \:=\:3 & \Rightarrow & x \:=\:\ln 3 \\ e^x-4 \:=\:0 & \Rightarrow & e^x \:=\:4 & \Rightarrow & x \:=\:\ln4 \end{Bmatrix}$