Solve an eqation, two unknowns, just need them as a ratio x/y?

Question

Hi, I'm trying to do some geochemistry homework, and I need to plot something as Log ([x]/[y]) vs Log[z], in the eqation I'm having trouble with there's no z though so I just need to find what log([x]/[y]) is.

My equation is 1/([Na]^2)*[H] = 10^109.4

Not much but I sort of worked to:

-2log[Na] = log[H]+109.4

I I just can't get rid of the -2 though, away from the Na, and join the Na and H so that it's Na / H = ans

I tried the year 10 stuff, squaring both sides, and on and on..

I feel like I'm missing some mathamatic tool. Or maybe something simple

* 41 minutes ago
* - 4 days left to answer.

Additional Details
Thanks for the answer but I'm actually plotting log([Na+]/[H+]) vs log [H4SiO4]

I have lots of chemical equations to plot, though in this one there is no [H4SiO4], so I just need to find what log([Na+]/[H+]) is equal to and then plot that as a horizontal line.

So I just need to re-arange so I have (x/y = something) even. Then I can just take the log
(Log10 btw)

For background I'm constructing a mineral stability diagram.

Answer 1

You can't.



You're looking for log([Na+]/[H+]) to equal some constant number so you can plot it against [H4SiO4] as a horizontal line. But log([Na+]/[H+]) is not constant.



You started from [Na]^2 * [H] = constant

You cannot turn that into [Na] / [H] = constant



for example, if [H] = 10^-109.4 then [Na] = 1 and [Na] / [H] = 10^109.4

but if [H] = 1 then [Na] = 10^-54.7 and [Na] / [H] = 10^-54.7





It does not make sense in this case to plot log([Na+]/[H+]) vs log [H4SiO4]. Perhaps you need to plot log[Na+] vs log[H+] instead. Or perhaps the H4SiO4 is the source of the H+ and there's a dependency you didn't realize?

Answer 2

If you ever took precalculus or some other math class which covers properties of functions, you learn how to determine the domain of the function. One of the red flags to look out for is when you divide by zero. In your expression, when x = 3, the denominator is zero. Thus, the domain is every number beside 3. Unfortunately, the number you are trying to plug in (x = 3) is the only number that doesn't work in this function. To see this first hand, you0 can graph this function on a TI-83. If you zoom in on the point of the graph at x = 3, you will see that there is a blank spot there! That is because, as stated above, there just isn't a value of the expression at x = 3. You may say, well it looks like the answer should be 6, looking at the graph. This concept of what the answer "should be" is what limits are all about. The values of the function on the left and right of x = 3 all go towards 6 as you get closer and closer. So we say the limit as x goes to 3 is 6. So even though it is not technically the answer, 6 is your best choice. Zero is absolutely not correct in any sense. The very best answer is to say that the expression is undefined at x = 3. This problem illustrates why 0/0 is called indeterminate. In this problem, 0/0 in a way equals 6. The idea that 0/0 can equal anything is actually the essence of calculus.

Answer 3

The plot of -2log (x ) - log (x) - 109.4 is:

http://s697.photobucket.com/albums/vv335/thevip/log1.jpg