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Finding domain with e functions help

bart11

New member
Feb 13, 2012
6
I'm asked to find the domain of 1/[e^(x+y)-3]

Which means I'm solving for e^(x+y)>=3

But how would I go about solving this?
 

pickslides

Member
Feb 1, 2012
57
e^(x+y) = e^y*e^x
 

bart11

New member
Feb 13, 2012
6

pickslides

Member
Feb 1, 2012
57
This is supposed to help you separate x & y so you can find a function in the form of y = f(x) and find the domain from there.
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
I'm asked to find the domain of 1/[e^(x+y)-3]

Which means I'm solving for e^(x+y)>=3

But how would I go about solving this?
The only possible "difficulty" with that is that you cannot divide by 0. That, in turn, means that e^{x+y} cannot be equal to 3. So, what can x+ y not be equal to?

(To solve e^x= a, take the natural logarithm of both sides.)

Pickslide's observation that e^{x+y}= e^xe^y is true but I don't believe using that is particularly useful here.
 
Last edited:

The Chaz

Member
Jan 26, 2012
24
CodeCogsEqn.gif

Then taking (natural) logs on both sides, we find that

CodeCogsEqn.gif