dongkim2 and EdWood:
First of all EdWood, kudos to you on your screenname. If nothing else, "Plan 9 From Outer Space" and "Glen or Glenda" provided fodder for Tim Burton's best movie.
But back to math...you guys have it right. 5^x = 11^y cannot be true unless both x and y are 0. I like EdWood's method of thinking about the units digits.
You can also consider prime factorization (my single favorite topic on the GMAT!)...
5^x will be some power of 5, since x is an integer, and any power of 5 breaks down into a prime factorization that includes only 5's (no 11's). Same with 11^y (no 5's as prime factors).
So the only way 5^x could possibly equal 11^y is if both x and y are 0, thus eliminating prime factors altogether.
blaster:
Applying the n-equations, n-variables rule is a great instinct to have, so it's great you've developed that. However, that rule applies strictly to LINEAR EQUATIONS. Because we're dealing with exponents here, the rule does not apply.
Another example would be quadratics. x^2 = 4 is a single equation with a single variable, but it produces two possible x values, because the equation is not linear.
Make sense?
Rich Zwelling
GMAT Instructor, Veritas Prep
