Find $x$: $3^{x} + 3^{x} + 3^{x} = 243$.

Find $x$: $3^{x} + 3^{x} + 3^{x} = 243$.
  1. $4$
  2. $5$
  3. $3$
  4. $81$

Solution

$3 \cdot 3^{x} = 3^{x+1} = 243 = 3^{5}$, so $x + 1 = 5 \Rightarrow x = 4$.

Asked in: IMO

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