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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