$\sum\limits_{n = 1}^n {{1 \over {{{\log }_{{2^n}}}(a)}}} = $

  • A

    ${{n(n + 1)} \over 2}{\log _a}2$

  • B

    ${{n(n + 1)} \over 2}{\log _2}a$

  • C

    ${{{{(n + 1)}^2}{n^2}} \over 4}{\log _2}a$

  • D

    None of these

Similar Questions

The number of solution pairs $(x, y)$ of the simultaneous equations $\log _{1 / 3}(x+y)+\log _3(x-y)=2$ $2^{y^2}=512^{x+1}$ is

  • [KVPY 2017]

The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -

The value of ${\log _2}.{\log _3}....{\log _{100}}{100^{{{99}^{{{98}^{{.^{{.^{{{.2}^1}}}}}}}}}}}$ is

The interval of $x$ in which the inequality ${5^{(1/4)(\log _5^2x)}}\, \geqslant \,5{x^{(1/5)(\log _5^x)}}$

The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^2 \geq 0$ is

  • [JEE MAIN 2023]