Simultaneous equations with x and y exponents

• November 3rd 2009, 04:10 AM
Stuck Man
Simultaneous equations with x and y exponents
Is there a way of doing these?
• November 3rd 2009, 04:36 AM
Jameson
That depends.

It's a good idea to ask for specific examples rather than really general questions. It's hard to answer statements like the one you wrote here.

The answer to your question depends on if you mean by hand vs. computer, only basic algebra versus logarithms, etc.
• November 3rd 2009, 06:57 AM
Stuck Man
e^x + 3e^y = 3
e^2x - 9e^2y = 6

The answer has to be expressed as logs to base e.

I have the answers and they seem to be correct.
• November 3rd 2009, 07:09 AM
alexmahone
Quote:

Originally Posted by Stuck Man
e^x + 3e^y = 3
e^2x - 9e^2y = 6

The answer has to be expressed as logs to base e.

I have the answers and they seem to be correct.

$e^x+3e^y=3$

$e^{2x}-9e^{2y}=6$

$(e^x)^2-(3e^y)^2=6$

$(e^x+3e^y)(e^x-3e^y)=6$

$3(e^x-3e^y)=6$

$e^x-3e^y=2$

$2e^x=5$

$e^x=\frac{5}{2}$

$x=ln (\frac{5}{2})$

$6e^y=1$

$e^y=\frac{1}{6}$

$y=ln(\frac{1}{6})=-ln 6$
• November 4th 2009, 03:42 AM
Stuck Man
Thanks.