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
(y1)(3y2) = 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
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