solving for x and y exponent
Author
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.
Author
but I'm not sure why. I just took the hint and worked from there but I don't get why that works.
Author
nevermind after I thought about it for longer I understand. thanks a lot for helping.
Quote:Original post by subflood
but 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].
Quote:Original post by subflood
but 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].
[edit] Above AP was me, too. [/edit]
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. ;)
Quote:Original post by darookie
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].
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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