MCQ
If $\frac{2^{x-1} \times 4^{2 x+1}}{8^{x-1}}=64$ then x is equal to
- ✓1
- B2
- C-2
- D3
✓
Answer
Correct option: A.
1
(a)
We have,
$\begin{aligned} & \frac{2^{x-1} \times 4^{2 x+1}}{8^{x-1}}=64 \Rightarrow \frac{2^{x-1} \times\left(2^2\right)^{2 x+1}}{\left(2^3\right)^{x-1}}=64 \Rightarrow \frac{2^{x-1} \times 2^{2(2 x+1)}}{2^{3(x-1)}}=2^6 \Rightarrow \frac{2^{x-1+4 x+2}}{2^{3 x-3}}=2^6 \\ \Rightarrow \quad & \frac{2^{5 x+1}}{2^{3 x-3}}=2^6 \Rightarrow 2^{5 x+1} \times 2^{-3 x+3}=2^6 \Rightarrow 2^{5 x+1-3 x+3}=2^6 \Rightarrow 2 x+4=6 \Rightarrow 2 x=2 \Rightarrow x=1\end{aligned}$
We have,
$\begin{aligned} & \frac{2^{x-1} \times 4^{2 x+1}}{8^{x-1}}=64 \Rightarrow \frac{2^{x-1} \times\left(2^2\right)^{2 x+1}}{\left(2^3\right)^{x-1}}=64 \Rightarrow \frac{2^{x-1} \times 2^{2(2 x+1)}}{2^{3(x-1)}}=2^6 \Rightarrow \frac{2^{x-1+4 x+2}}{2^{3 x-3}}=2^6 \\ \Rightarrow \quad & \frac{2^{5 x+1}}{2^{3 x-3}}=2^6 \Rightarrow 2^{5 x+1} \times 2^{-3 x+3}=2^6 \Rightarrow 2^{5 x+1-3 x+3}=2^6 \Rightarrow 2 x+4=6 \Rightarrow 2 x=2 \Rightarrow x=1\end{aligned}$
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
The area of an equilateral triangle is $81\sqrt{3}\text{cm}^2.$ Its height is:
→- $9\sqrt{3}\text{cm}$
- $6\sqrt{3}\text{cm}$
- $18\sqrt{3}\text{cm}$
- $9\text{cm}$
Write the correct answer in the following:
Euclid belongs to the country:
Euclid belongs to the country:
- Babylonia.
- Egypt.
- Greece.
- India.
Which of the following is a polynomial ?
If $\bar{\text{x}}_1, \bar{\text{x}}_2, \bar{\text{x}}_3, ....., \bar{\text{x}}_\text{n}$ are the means of n group with n1, n2, ...., nn number of observations respectively, then the mean $\bar{\text{x}}$ of all the groups taken together is given by:
→- $\sum\limits^\text{n}_{\text{i}=1}$
- $\frac{\sum\limits^\text{n}_{\text{i}=1}\text{n}_\text{i}\bar{\text{x}}_\text{i}}{\text{n}^2}$
- $\frac{\sum\limits^\text{n}_{\text{i}=1}\text{n}_\text{i}\bar{\text{x}}_\text{i}}{\text{n}_2}$
- $\frac{\sum\limits^\text{n}_{\text{i}=1}\text{n}_\text{i}\bar{\text{x}}_\text{i}}{2\text{n}}$
The sides of a triangle are 35cm, 54cm and 61cm respectively, and its area is $420\sqrt{5}\text{cm}^2.$ The length of its longest altitude is:
→The graph of x = 4 is a line:
The simplest for of $1.\overline{6}$ is:
→→
In a $\triangle A B C, \angle A=50^{\circ}$ and BC is produced to a point D. If the bisectors of $\angle A B C$ and $\angle A C D$ meet at $E$, then $\angle E=$
→The number of dimensions of a surface are: