solving for x and y exponent

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here it goes: 2^4 x 3^5 x 4^3 = 2^x x 3^y what is value of x + y I'm not sure how I can get this. The 4^3 confuses me. Thanks for the help.

Hint: 4 = 2^2

x + y = 15??

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Quote:
 Original post by subfloodx + y = 15??

yes

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but I'm not sure why. I just took the hint and worked from there but I don't get why that works.

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nevermind after I thought about it for longer I understand. thanks a lot for helping.

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Quote:
 Original post by subfloodbut I'm not sure why. I just took the hint and worked from there but I don't get why that works.

well it's 24 x 35 x 43
43 can be substituted with (22)3.
According to the arithmetic rules of powers you get 22 x 3, which equals 26.

Now following the next rule you can multiply 24 and 26 by adding the exponents to get 210.

The final equation thus is 210 x 35 = 2x x 3y.

Trivial - you don't have to do a thing, except replacing 'x' and 'y' with their literal counterparts from the left side of the equation [smile].

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Quote:
 Original post by subfloodbut I'm not sure why. I just took the hint and worked from there but I don't get why that works.

well it's 24 x 35 x 43
43 can be substituted with (22)3.
According to the arithmetic rules of powers you get 22 x 3, which equals 26.

Now following the next rule you can multiply 24 and 26 by adding the exponents to get 210.

The final equation thus is 210 x 35 = 2x x 3y.

Trivial - you don't have to do a thing, except replacing 'x' and 'y' with their literal counterparts from the left side of the equation [smile].

 Above AP was me, too. [/edit]

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It would be far less trivial to actually prove this (x,y) solution is unique. If it's not the case you can't tell what x+y is. ;)

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Quote:
 Original post by darookieThe final equation thus is 210 x 35 = 2x x 3y.Trivial - you don't have to do a thing, except replacing 'x' and 'y' with their literal counterparts from the left side of the equation [smile].

Actually that's wrong. The solution for x is:

x = log_2(1024 * 3^(5-y))

For example if you take y = 5 then you have the answer you arrived at: x = 10. But if you take y = 6 then x = 10 - log_2(3), for y = 7, x = log_2(1024/9) and so on.

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