Solve $9^{x} = 27^{2}$.

Solve $9^{x} = 27^{2}$.
  1. $2$
  2. $3$
  3. $\dfrac{3}{2}$
  4. $6$

Solution

Use base 3: $(3^{2})^{x} = (3^{3})^{2} \Rightarrow 3^{2x} = 3^{6} \Rightarrow 2x = 6 \Rightarrow x = 3$.

Asked in: IMO

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