Sign in to follow this  
subflood

solving for x and y exponent

Recommended Posts

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.

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
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].

Share this post


Link to post
Share on other sites
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]

Share this post


Link to post
Share on other sites
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. ;)

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
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.

Share this post


Link to post
Share on other sites
Quote:
Original post by Anonymous Poster
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.

No, it's not. It's a perfectly valid transformation.
Quote:

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.

That was not the problem. The (or one) value of x + y was to be found. You provided a representation of x in terms of y. Typical case of thinking in the wrong direction [smile]. BTW. the interesting thing is what Charles B. pointed out - prove that 15 is a unique solution of x + y.

[edit]
Actually I think this is a textbook question that shall make readers familiar with the arithmetic rules of powers. Otherwise it would have been formulated quite differently.
[/edit]

[Edited by - darookie on October 5, 2004 7:48:33 AM]

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
Quote:
Original post by darookie
... BTW. the interesting thing is what Charles B. pointed out - prove that 15 is a unique solution of x + y.

That's exactly what the previous poster was trying to say.

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
(I mean that 15 is not the only solution.)

My question is: are there any complex solutions? why?

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
On second thought, it's obvious that if
x = 10 + (5-y)log2(3)
then for any (real or complex) y there exists one x (also real or complex).

Share this post


Link to post
Share on other sites
Quote:
Original post by Anonymous Poster
(I mean that 15 is not the only solution.)

My question is: are there any complex solutions? why?

Hint: x + y*log23 = 10 + 5*log23

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this