If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to

  • A

    $125$

  • B

    ${a^2}$

  • C

    $25$

  • D

    None of these

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  • [JEE MAIN 2023]

If ${x_n} > {x_{n - 1}} > ... > {x_2} > {x_1} > 1$ then the value of ${\log _{{x_1}}}{\log _{{x_2}}}{\log _{{x_3}}}.....{\log _{{x_n}}}{x_n}^{x_{n - 1}^{{ {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} ^{{x_1}}}}}$ is equal to