If x and y are positive numbers such that and , then the value of x is
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This one took me way longer than it should have. The trick with substituting y=9x and then getting the exponents to match is not something I would spot under time pressure. Respect to anyone who nails this in under 2 min.
Same. I stared at it for a while before realizing you have to rewrite 9 as 3^2.
Yeah the 705+ label is no joke here.
Once you substitute y = 9x into x^y = y^x, how do you decide which side to simplify first? I keep getting tangled up with the 9x term.
Try taking both sides to some common base, the 9 is the key.
Nice question. The exponents here are nasty but the base manipulation is clean. Definitely saving this one for review.
Got it, but only after guessing and checking the answer choices. Is there a faster algebraic route, or is back-solving the intended approach at this level?
What it tests
Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.
Common trap
Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).