If $x, y, z$ are in harmonic progression,then $\log(x + z) + \log(x - 2y + z) = \dots$

If $a, b, c$ are in harmonic progression,then $\frac{a-b}{b-c} = \dots$

If ${x^a} = {x^{b/2}}{z^{b/2}} = {z^c}$,then $a, b, c$ are in

If $a^x = b^y = c^z$ and $a, b, c$ are in $G.P.$,then $x, y, z$ are in

If $x_1, x_3$ are the roots of $A x^2 - 4 x + 1 = 0$ and $x_2, x_4$ are the roots of $B x^2 - 6 x + 1 = 0$ such that $x_1, x_2, x_3, x_4$ are in harmonic progression,then $\frac{B+A}{B-A} = $

If $p, q, r$ are in harmonic progression and $p$ and $r$ are distinct and have the same sign,then what is the nature of the roots of the equation $px^2 + 2qx + r = 0$?