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MathNet 2023-part-04 — 191 problems (EN–VI) Question 106

Math Olympiad Vault · MathNet 2023-part-04 — 191 problems (EN–VI)

Question 106

Find the sum of the smallest and largest possible values for $x$ which satisfy the following equation.

$$9^{x + 1} + 2187 = 3^{6x - x^{2}}$$