MCQ
If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
  • A
    $125$
  • B
    ${a^2}$
  • $25$
  • D
    None of these

Answer

Correct option: C.
$25$
c
(c) ${\log _5}a.{\log _a}x = 2$   $\Rightarrow $ ${\log _5}x = 2$

$ \Rightarrow $ $x = {5^2} = 25$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The equations of the tangents to circle $5{x^2} + 5{y^2} = 1$, parallel to line $3x + 4y = 1$ are
A straight line through the vertex $P$ of a triangle $P Q R$ intersects the side $Q R$ at the point $S$ and the circumcircle of the triangle $P Q R$ at the point $T$. If $S$ is not the centre of the circumcircle, then

$(A)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}<\frac{2}{\sqrt{\mathrm{QS} \times \mathrm{SR}}}$

$(B)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}>\frac{2}{\sqrt{\mathrm{QS} \times \mathrm{SR}}}$

$(C)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}<\frac{4}{\mathrm{QR}}$

$(D)$ $\frac{1}{\mathrm{PS}}+\frac{1}{\mathrm{ST}}>\frac{4}{\mathrm{QR}}$

Let $a_1, a_2 , a_3,.....$ be an $A.P$, such that $\frac{{{a_1} + {a_2} + .... + {a_p}}}{{{a_1} + {a_2} + {a_3} + ..... + {a_q}}} = \frac{{{p^3}}}{{{q^3}}};p \ne q$. Then $\frac{{{a_6}}}{{{a_{21}}}}$ is equal to
Let $C$ be the circle $x^2+y^2=1$ in the $X Y$-plane. For each $t \geq 0$, let $L_t$ be the line passing through $(0,1)$ and $(t, 0)$. Note that $L_t$ intersects $C$ in two points, one of which is $(0,1)$. Let $Q_t$ be the other point. As $t$ varies between 1 and $1+\sqrt{2}$, the collection of points A $_t$ sweeps out an arc on $C$. The angle subtended by this arc at $(0,0)$ is
Let $a \in R$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{\frac{1}{4}} x+a=0$. If $\alpha^4+\beta^4=-30$, then the product of all possible values of $a$ is $......$
Let $S=\left\{z \in C : z^{2}+\bar{z}=0\right\}$. Then $\sum \limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))$ is equal to$......$
The set of all real values of $\lambda$ for which the function $f(x)=\left(1-\cos ^{2} x\right) \cdot(\lambda+\sin x)$ $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right),$ has exactly one maxima and exactly one minima, is
Let $\phi (x) = (f(x))^3 -3(f(x))^2 + 4f(x) + 5x + 3 \sin x + 4 \cos x\, \forall \, x \in R$, then -
Let $A :\{1,2,3,4,5,6,7\}$. Define $B =\{ T \subseteq A$ : either $1 \notin T$ or $2 \in T \}$ and $C = \{ T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $\}$. Then the number of elements in the set $B \cup C$ is $\dots\dots$
If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$, then the number of relations from $A$ to $B$ is