Logressions

Algebra Level 4

x,y,zx,y,z are real numbers that satisfy the equation below

log(x2y+z)+log(x+z)=2log(xz)\large \log (x-2y+z)+\log (x+z)=2\log (x-z)

What kind of progression do x,y,zx,y,z form?

Details and Assumptions

  • APAP denotes Arithmetic Progression

  • GPGP denotes Geometric Progression

  • HPHP denotes Harmonic Progression

  • AGPAGP denotes Arithmetic-Geometric Progression

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