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1969 AMC 12 Question 29

AMC12 · 1969 AMC 12

Question 29

If $x=t^{\frac{1}{t-1}}$ and $y=t^{\frac{t}{t-1}},$ $t\gt0,$ $t\ne1,$ a relation between $x$ and $y$ is:
  1. $y^x=x^{\frac{1}{y}}$
  2. $y^{\frac{1}{x}}=x^y$
  3. $y^x=x^y$
  4. $x^x=y^y$
  5. none of these