d
(d) Given, One root =$ 5$ and equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&{ - 2}\\7&8&x\end{array}\,} \right|\, = 0$.
Expanding the given equation, we get
$ + {\log _x}z({\log _y}x{\log _z}y - {\log _z}x)$
==> ${x^3} + 16x - 6x - 42 + 112 - 49x = 0$
==> ${x^3} - 39x + 70 = 0$
Since $ 5$ is the one root of given equation, therefore ${x^3} - 5{x^2} + 5{x^2} - 25x - 14x + 70 = 0$
==> ${x^2}(x - 5) + 5x(x - 5) - 14(x - 5) = 0$
==> $(x - 5)({x^2} + 5x - 14) = 0$
==> $(x - 5)\,(x - 2)\,(x + 7) = 0$ or $x = 5,\,2$ and $ -7.$