# Equation Proofs

• Feb 22nd 2011, 08:02 AM
360modina
Equation Proofs
I am having a lot of difficulty figuring this one out. The goal is to show that equations 1, 2, and 3, give the final simplified equation 4. I have always been more of a calculus person, and have trouble with these types of algebra problems.

http://rapidshare.com/files/449301420/GetEQ4.png

So far I have tried multiplying both S and Sigma together and attempted to put ga into the equation, which didn't really get me anywhere. Any help is appreciated!
• Feb 22nd 2011, 08:21 AM
Ackbeet
I would plug Equations 2 and 3 into 4 and show that you get Equation 1, for an appropriate choice of N. Then, since all your steps are reversible, you've shown that which you were asked to show.
• Feb 22nd 2011, 08:49 AM
360modina
I plugged both 2 and 3 into the last equation and it simplified to this:

http://rapidshare.com/files/449308643/GetEQ4part2.png

The exponents still look incorrect and I missing something?
• Feb 22nd 2011, 08:51 AM
Ackbeet
Nothing incorrect yet. Remember the laws of exponents, and simplify your expression a bit.
• Feb 22nd 2011, 09:18 AM
360modina
I was able to simplify the exponents a lot, and it looks better:
http://rapidshare.com/files/449313639/GetEQ4part3.png
I am still stuck with the ga term on the bottom though
• Feb 22nd 2011, 09:20 AM
Ackbeet
You should have

\$\displaystyle g_{a}^{n_{b}}\$ on the bottom.

You now must choose the value of \$\displaystyle N\$ that makes it all work the same as Equation # 1.
• Feb 22nd 2011, 09:24 AM
360modina
Correct, I just saw that I forgot to raise the bottom ga to the nb power, that makes so much more sense!
• Feb 22nd 2011, 09:26 AM
Ackbeet
So, what's N?
• Feb 22nd 2011, 09:31 AM
360modina
Would it happen to be N=\$\displaystyle n_b^2\$, that way the ga term on the bottom would disappear completely leaving only the ga^nb on the top?
• Feb 22nd 2011, 09:34 AM
Ackbeet
Not quite. You need to end up with \$\displaystyle g_{a}^{n_{a}}\$ on top. Right now, you have \$\displaystyle g_{a}^{N}\$ on top, and \$\displaystyle g_{a}^{n_{b}}\$ on the bottom. Use the laws of exponents. What must \$\displaystyle N\$ be?
• Feb 22nd 2011, 10:14 AM
360modina
N=\$\displaystyle n_a+n_b\$
• Feb 22nd 2011, 10:18 AM
Ackbeet
There you go. I'd say you're done now, essentially. Just run your computations in reverse, and you can show that Equations 1-3 give you Equation 4.