Log Inequality

Algebra Level 4

Let x,y,zx,y,z be positive real numbers satisfying x,y,z>1x,y,z > 1. It is true that logy(xz)logz(xy)k\log_y(xz)\cdot\log_z(xy) \ge k for some real number kk. Find kk accurate to 3 decimal places.

Details and Assumptions

kk may possibly be an integer.

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