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