MCQ
If $(16)^{2 x+3}=(64)^{x+3}$, then $4^{2 x-2}=$
- A$64$
- ✓$256$
- C$32$
- D$512$
✓
Answer
Correct option: B.
$256$
We have to find the value of $4^{2 x-2}$ provided $(16)^{2 x+3}=(64)^{x+3}$
So,
$(16)^{2 x+3}=(64)^{x+3}$
$\left(2^4\right)^{2 x+3}=\left(2^6\right)^{x+3}$
$2^{8 x+12}=2^{6 x+18}$
Equating the power of exponents we get
$8 x+12=6 x+18$
$8 x-6 x=18-12$
$2 x=6$
$x=\frac{6}{2}$
$x=3$
The value of $4^{2 x-2}$ is
$=4^{2 x-2}$
$=4^{2 \times 3-2}$
$=4^{6-2}$
$=4^4$
$=256$
Hence the correct alternative is $b$ .
So,
$(16)^{2 x+3}=(64)^{x+3}$
$\left(2^4\right)^{2 x+3}=\left(2^6\right)^{x+3}$
$2^{8 x+12}=2^{6 x+18}$
Equating the power of exponents we get
$8 x+12=6 x+18$
$8 x-6 x=18-12$
$2 x=6$
$x=\frac{6}{2}$
$x=3$
The value of $4^{2 x-2}$ is
$=4^{2 x-2}$
$=4^{2 \times 3-2}$
$=4^{6-2}$
$=4^4$
$=256$
Hence the correct alternative is $b$ .
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $a+b+c=9$ and $a b+b c+c a=23$, then $a^3+b^3+c^3-3 a b c=$
→
In the figure $\ce{AB\ \&\ CD}$ are two straight lines intersecting at $\text{O , OP}$ is a ray. What is the measure of $\ce{\angle AOD}$.
→The remainder when $f(x)=x^5$ is divided by $g(x)=x^2-9$, is
→The number of angles formed by a transversal with a pair of parallel lines are.
Which of the following is a correct statement?
In the given figure, $ABCD$ is a cyclic quadrilateral in which $DC$ is produced to $E$ and $CF$ is drawn parallel to $AB$ such that $\angle\text{ADC}=95^\circ$ and $\angle\text{ECF}=20^\circ.$ Then, $\angle\text{EAD}=?$ 
→The point which lies on $x-$axis at a distance of $3$ units in the positive direction of $x-$axis is:
→Which one of the following is not equal to $\big(\sqrt[3]{8}\big)^{-\frac{1}{2}}?$
→The exterior angle of a triangle is equal to the sum of two:
If the bisectors of $\angle A$ and $\angle B$ of quadrilateral ABCD intersect each other at $P, \angle B$ and $\angle C$ at Q of $\angle C$ and $\angle D$ at R and of $\angle D$ and $\angle A$ at S, then PQRS is a
→