# Linear Intersecting Exponential

Algebra Level 2

Let $$A$$ and $$B$$ the two intersection points of the curve $$y=2 \cdot 3^x$$ and a line with slope $$1$$. Let $$\alpha$$ and $$\beta$$ $$(\alpha < \beta$$) be the $$x$$-coordinates of $$A$$ and $$B,$$ respectively. If the length of line segment $$AB$$ is $$4\sqrt{2}$$, what is the value of $$3^{\alpha}?$$

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