Download App

STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius $2$ . If the line of the common chord of $\mathrm{C}_1$ and $\mathrm{C}_2$ intersects the $\mathrm{y}$-axis at the point $\mathrm{P}$, then the square of the distance of $\mathrm{P}$ from the centre of $\mathrm{C}_1$ is :
→
The maximum value of $[x(x-1)+1]^{\frac{1}{3}}, 0 \leq x \leq 1$ is
→
For the $LP$ problem

"Maximize $z=x+4 y$

subject to $3 x+6 y \leq 6,4 x+8 y \geq 16$ and $x \geq 0, y \geq 0$."

→
Let $\alpha \in(0,1)$ and $\beta=\log _{ c }(1-\alpha)$. Let $P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots . .+\frac{x^n}{n}, x \in(0,1)$ Then the integral $\int \limits_0^\alpha \frac{ t ^{50}}{1- t } dt$ is equal to
→
Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x \in R$. Then the set of all $x$ satisfying $(f \circ g \circ g \circ f)(x)=(g \circ g \circ f)(x)$, where $(f \circ g)(x)=f(g(x))$, is
→
The value of $\cos 52^\circ + \cos 68^\circ + \cos 172^\circ $ is
→
The values of $\lambda$ and $\mu$ for which the system of linear equations

$x+y+z=2$

$x+2 y+3 z=5$

$x+3 y+\lambda z=\mu$

has infinitely many solutions are, respectively

→
The position of the points $(3, 4)$ and $(2, -6)$ with respect to the line $3x - 4y = 8$ are
→
If $\sin \theta = \frac{{12}}{{13}},(0 < \theta < \frac{\pi }{2})$ and $\cos \phi = - \frac{3}{5},\left( {\pi < \phi < \frac{{3\pi }}{2}} \right)$. Then $\sin (\theta + \phi )$will be
→
If $A = \left[ {\begin{array}{*{20}{c}}3&5\\2&0\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}1&{17}\\0&{ - 10}\end{array}} \right]$ then $|AB|$ is equal to
→