Let's progress arithmetically

Algebra Level pending

The real numbers $$x, y, t$$ in this order, form a AP with common difference $$r$$. Be $$n$$ a positive real number and other than 1. Assuming that $$\large 3{ n }^{ x }+2{ n }^{ y }-{ n }^{ t }=0$$ is true, find the common diference.

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