If x = _2 ( 56 + 56 + 56 + .... + ) then - Vidyadip

MCQ

If $x = {\log _2}\left( {\sqrt {56 + \sqrt {56 + \sqrt {56 + .... + \infty } } } } \right)$ then

A
$x < 0$
B
$0 < x < 2$
✓
$2 < x < 4$
D
$3 < x < 4$

✓

Answer

Correct option: C.

$2 < x < 4$

c
$x=\log _2(\sqrt{56+\sqrt{56+\ldots \infty}})$

het $t=\sqrt{56+t}$

$t^2-t-56=0$

$(t+7)(t-8)=0$

$t=8,-7 \quad$ [log can't be negative]

$\therefore x=\log _2 8$

$\therefore x=3$ (c)

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 1. relation and function→1. relation and function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If A is 3×4 matrix and B is a matrix such that A'B and BA' are both defined. Then, B is of the type:

3×4
3×3
4×4
4×3

Let $f: I R \rightarrow I R$ be defined as $f(x)=|x|+\left|x^2-1\right|$. The total number of points at which $f$ attains either a local maximum or a local minimum is

If $l\,a + m\,b + n\,c = 0,$ where $l,\,m,\,\,n$ are scalars and $a, b, c $ are mutually perpendicular vectors, then

$\int_0^{\pi /2} {\frac{{x + \sin x}}{{1 + \cos x}}\,dx = } $

The function ${{a\sin x + b\cos x} \over {c\sin x + d\,\cos x}}$ is decreasing, if

If $f(x)=\frac{\left(\tan 1^{\circ}\right) x+\log _{\varepsilon}(123)}{x \log _{\varepsilon}(1234)-\left(\tan 1^{\circ}\right)}, x > 0$, then the least value of $f(f(x))+f\left(f\left(\frac{4}{x}\right)\right)$ is $...........$.

If $z = {y \over x}\left[ {\sin {x \over y} + \cos \left( {1 + {y \over x}} \right)} \right]$, then $x{{\partial z} \over {\partial x}} = $

If $f(x)=\cos ^{-1} \sqrt{x}$, 0 < x < 1, which of the following is aqual to $f^{\prime}(x) ?$

A curve is such that the area of the region bounded by the co-ordinate axes, the curve $\&$ the ordinate of any point on it is equal to the cube of that ordinate. The curve represents

If $f : R \rightarrow R$ be a continuous function satisfying

$\int \limits_0^{\pi / 2} f(\sin 2 x) \cdot \sin x d x+\alpha \int \limits_0^{\pi / 4} f(\cos 2 x) \cdot \cos x d x=0$then $\alpha$ is equal to