# Thread: Simultaneous equations with x and y exponents

1. ## Simultaneous equations with x and y exponents

Is there a way of doing these?

2. 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.

3. 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.

4. 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.
$\displaystyle e^x+3e^y=3$

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

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

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

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

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

$\displaystyle 2e^x=5$

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

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

$\displaystyle 6e^y=1$

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

$\displaystyle y=ln(\frac{1}{6})=-ln 6$

5. Thanks.