If $9^{x} \cdot 9^{x} \cdot 9^{x} = 729^{2}$, find $x$.

If $9^{x} \cdot 9^{x} \cdot 9^{x} = 729^{2}$, find $x$.
  1. $1$
  2. $2$
  3. $3$
  4. $6$

Solution

$9^{3x} = (9^{3})^{2} = 9^{6}$, so $3x = 6 \Rightarrow x = 2$.

Asked in: IMO

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