Several old logarithmic and other problems

I need to correct a test that I failed. Most questions I can figure out by now, but these ones I can't. They are supposed to be Algebra review, but apparently I didn't pay enough attention. Can I get an explanation on how to do these problems?

1. Solve:

log xy = 5/log z

log yz = 8/log x

log zx = 9/log y

2. Find all pairs of integers such that x^3 + y^3 = 2011

3. Find all integers x where x^2-x+1 divides x^2012+x+2001

4. f(x) is the digits of x reversed. ex: f(123) = 321

Find all 3 digit numbers where f^2(x)-x^2 is the cube of a positive integer.

5. 2x^2+3xy+2x^2 is less than or equal to 7

max(2x+y, x+2y) is less than or equal to 4.

x and y must be real.

This is my first post on this forum, I hope I didn't break any rules. Our teacher does permit external help for test corrections.

Thanks!

Re: Several old logarithmic and other problems

Hello, JohnDyer!

We have: .

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Re: Several old logarithmic and other problems

Thank you so much Soroban! That was more difficult than I expected, I don't think I would have figured it out myself.

Any help on the other question?

Re: Several old logarithmic and other problems

Sorry for bumping so soon, but I need this by tonight if possible.

Yes, I do realize that nobody on this forum is paid to help, but it would be nice to have this done. These 20 point will make or break my quarterly grade.

Thanks!