How to determine the value of two constants among lot of equations?

Hello. I want to determine the value of two constants X and Y, among a lot of equations. I mean, equations such as:

2^X=3*Y
4^X=5*Y
7^X=10*Y
15^X=34*Y

..... and more.

How THE value of X and Y? Thank you very much!

[Matt Kindig]

Are you looking for a single value for X and Y that satisfy all of these equations? Because there does not exist a unique solution that satisfies all four of the equations you've shown.

If you take the equations two at a time, you can just use algebra to solve for X and Y by hand. I just did it, and unless my math is wrong:

Given: b1^X = a1*Y;   b2^X = a2*Y
Solution:   X = log(a1/a2)/log(b1/b2); Y = (1/3)*2^X

Answer 1

[Matt J]

If you take the log of both sides, you will get linear equations in X and log(Y), e.g., your first 2 equations become

 X*log2-log(Y)=log(3)
 X*log4-log(Y)=log(5)

so you can solve using MATLAB's usual linear equation solvers

 xlogy = [log([2;4]),-ones(2,1)]\log([3;5]);

 x=xlogy(1), y=exp(xlogy(2))

[Matt J]

For more than 2 equations, this will give you a least squares fit to X and log(Y). You'll have to decide whether that's what you want.