The value of $x$ satisfying ${\log _a}x + {\log _{\sqrt a }}x + {\log _{3\sqrt a }}x + .........{\log _{a\sqrt a }}x = \frac{{a + 1}}{2}$ will be

  • A

    $x = a$

  • B

    $x = {a^a}$

  • C

    $x = {a^{ - 1/a}}$

  • D

    $x = {a^{1/a}}$

Similar Questions

If $p$ times the ${p^{th}}$ term of an $A.P.$ is equal to $q$ times the ${q^{th}}$ term of an $A.P.$, then ${(p + q)^{th}}$ term is

Suppose that the number of terms in an $A.P.$ is $2 k$, $k \in N$. If the sum of all odd terms of the $A.P.$ is $40 ,$ the sum of all even terms is $55$ and the last term of the $A.P.$ exceeds the first term by $27$ , then $k$ is equal to

  • [JEE MAIN 2025]

If the $10^{\text {th }}$ term of an A.P. is $\frac{1}{20}$ and its $20^{\text {th }}$ term is $\frac{1}{10},$ then the sum of its first $200$ terms is

  • [JEE MAIN 2020]

If the sum of $n$ terms of an $A.P.$ is $3 n^{2}+5 n$ and its $m^{\text {th }}$ term is $164,$ find the value of $m$

Find the sum of all natural numbers lying between $100$ and $1000,$ which are multiples of $5 .$