Posted by **Kyle** on Friday, January 11, 2013 at 1:28am.

How do you simplify:

5*e^(-10x) - 3*e^(-20x) = 2

I'm not sure if I can take natural log of both sides to bring down the exponents.

- Calculus -
**Reiny**, Friday, January 11, 2013 at 8:16am
I will assume you want to "solve" for x

let e^(-10x) = y , then e^(-20x) = (e^(-10x)^2 = y^2

then you have

5y - 3y^2 = 2

3y^2 - 5y + 2 = 0

(y-1)(3y-2) = 0

y = 1 or y = 2/3

so e^(-10x) = 1 or e^(-10x) = 2/3

if e^(-10x) = 1

ln e^(-10x) = ln 1 = 0

-10x lne = 0

-10x = 0

x = 0

if e^(-10x) = 2/3

...

-10x = ln2 - ln3

x = -(l2 - ln3)/10 = appr .04055

## Answer this Question

## Related Questions

- Math - h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h...
- Pre calculus - Okay, I'm really fuzzy about my log and exponential chapter. For...
- check! - here is the question: log5(x-4)= log7x solve for x. These are just base...
- Chemistry - How do you do the inverse of absolute temperature? My kelvin ...
- calculus - solve the following equation. log 1/6 (x^2+x)- log 1/6 (x^2-x)=2 **...
- simplify - how do i simplify 10x^2y/-5x^4y Do you notice the y in both numerator...
- pre-calculus - What is the base of the function F(x) = b to the power of x if ...
- Exponents-word problem - A culture starts at 8600 bacteria. After one hour the ...
- math,factoring,help - Can someone please show me step by step how to do these. I...
- math - I need help figuring out these two questions on euations with integers. -...