If _x a, ; a^ x/2 and _b x are in G.P., then x = - Vidyadip

MCQ

If ${\log _x}a,\;{a^{x/2}}$ and ${\log _b}x$ are in $G.P.$, then $x = $

A
$ - \log ({\log _b}a)$
B
$ - {\log _a}({\log _a}b)$
✓
${\log _a}({\log _e}a) - {\log _a}({\log _e}b)$
D
${\log _a}({\log _e}b) - {\log _a}({\log _e}a)$

✓

Answer

Correct option: C.

${\log _a}({\log _e}a) - {\log _a}({\log _e}b)$

c
(c) Obviously ${({a^{x/2}})^2} = {\log _x}a\;.\;{\log _b}x = {\log _b}a$

$ \Rightarrow $${a^x} = {\log _b}a$

$ \Rightarrow $$x = {\log _a}({\log _b}a)$

$ \Rightarrow $$x = {\log _a}\left( {\frac{{{{\log }_e}a}}{{{{\log }_e}b}}} \right) = {\log _a}({\log _e}a) - {\log _a}({\log _e}b)$.

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

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 8. sequence and series→STD 11 - 8. sequence and series — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

$ABC$ is an isosceles triangle inscribed in a circle of radius $r$ . If $AB = AC $ $\& h$ is the altitude from $A$ to $BC$ and $P$ be the perimeter of $ABC$ then $\mathop {lim}\limits_{h \to 0} $ $\frac{\Delta }{{{P^3}}}$ equals (where $\Delta$ is the area of the triangle)

If the mean deviation about the median of the numbers $a,2a,3a,\;.\;.\;.\;.,50a$ is $50 $ thne $|a| $ equals

In an experiment with $15$ observations on $x$, the following results were available $\sum {x^2} = 2830$, $\sum x = 170$. On observation that was $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is..

The locus of the intersection point of $x\cos \alpha - y\sin \alpha = a$ and $x\sin \alpha - y\cos \alpha = b$ is

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\alpha \;x}} - {e^{\beta \;x}}}}{x} = $

The locus of a point which moves so that it is always equidistant from the point $A(a, 0)$ and $B (-a, 0)$ is

The equation of circle passing through the points $(1, \sqrt 2 ), (7,\sqrt 2 )$ and $(1, 3)$ is

If $|{x^2} - x - 6| = x + 2$, then the values of $x$ are

$P$ is a point on the parabola $y^2 = 4ax$ $ (a > 0)$ whose vertex is $ A$ . $PA $ is produced to meet the directrix in $D$ and $M$ is the foot of the perpendicular from $ P$ on the directrix. If a circle is described on $MD$ as a diameter then it intersects the $x-$ axis at a point whose co-ordinates are :

The coefficient of $\frac{1}{x}$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is