\(x,y,z\) are real numbers that satisfy the equation below

\[\large \log (x-2y+z)+\log (x+z)=2\log (x-z)\]

What kind of progression do \(x,y,z\) form?

**Details and Assumptions**

\(AP\) denotes Arithmetic Progression

\(GP\) denotes Geometric Progression

\(HP\) denotes Harmonic Progression

\(AGP\) denotes Arithmetic-Geometric Progression

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