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Orha
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Ok, first week of first year of undergraduate physics lab and they explain that we want all our graphs to be linear, and in order to do that we can change our x and y axes to be log(x) or y^2 or whatever. They did some simple examples such as y=(k/x)+c and explained that if the x axes is 1/x we get a linear graph.
1. Homework Statement
Homework time and they gave us: xy=a*exp(bxy) (where a,b are unknowns that we need to explain how we can figure them out using the to be linear function and the slope/intersection with y axes).
The problem is I wasn't able to separate x from y and make it look like a linear function.
Another question was bx = y/(a-y)
Here I could separate x from y (it is already done when given) but I can't get a situation where they are separate and non aren't dependent on a or b (it is simple to get to y=bxa/(1+bx) but x is dependent on b so I can't redefine the x axes properly)
I am sure I am misunderstanding something, or missing some kind of trick, but too many hours have been spent and I can't see it.
Any help would be greatly appreciated! Thanks in advance for any input!
ln and power rules
I tried ln the equation and got to ln(xy)=ln(a*exp(bxy)) => ln(x)+ln(y)=ln(a)+bxy
I've played around with this but always found myself back there. I can't seem to separate x and y so I can have an equation in the shape of y=mx+c (where I don't mind if y is ln(y) or even ln(y)/y or any kind of combination, and same goes for x, and m and c can be any combination of a and b).
For bx=y/(a-y) I explained above my problem.
Thanks again for any input or help, me and my friends are starting to climb on walls trying to figure out what we are missing.
1. Homework Statement
Homework time and they gave us: xy=a*exp(bxy) (where a,b are unknowns that we need to explain how we can figure them out using the to be linear function and the slope/intersection with y axes).
The problem is I wasn't able to separate x from y and make it look like a linear function.
Another question was bx = y/(a-y)
Here I could separate x from y (it is already done when given) but I can't get a situation where they are separate and non aren't dependent on a or b (it is simple to get to y=bxa/(1+bx) but x is dependent on b so I can't redefine the x axes properly)
I am sure I am misunderstanding something, or missing some kind of trick, but too many hours have been spent and I can't see it.
Any help would be greatly appreciated! Thanks in advance for any input!
Homework Equations
ln and power rules
The Attempt at a Solution
I tried ln the equation and got to ln(xy)=ln(a*exp(bxy)) => ln(x)+ln(y)=ln(a)+bxy
I've played around with this but always found myself back there. I can't seem to separate x and y so I can have an equation in the shape of y=mx+c (where I don't mind if y is ln(y) or even ln(y)/y or any kind of combination, and same goes for x, and m and c can be any combination of a and b).
For bx=y/(a-y) I explained above my problem.
Thanks again for any input or help, me and my friends are starting to climb on walls trying to figure out what we are missing.