- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
If $( \frac{1}{16})^{4-3x}\times 8^{x-2}=( 0.25)^x$, the find the value of $\frac{17x}{22}+1$.
Given: $( \frac{1}{16})^{4-3x}\times 8^{x-2}=( 0.25)^x$.
To do: To find the value of $\frac{17x}{22}+1$.
Solution:
$( \frac{1}{16})^{4-3x}\times 8^{x-2}=( 0.25)^x$
$\Rightarrow ( \frac{1}{2^4})^{4-3x}\times ( 2^3)^{x-2}=( \frac{25}{100})^x$
$\Rightarrow (2^{-4})^{4-3x}\times( 2^3)^{x-2}=( \frac{1}{4})^x$
$\Rightarrow ( 2)^{-4( 4-3x)}\times( 2)^{3( x-2)}=( \frac{1}{2^2})^x$
$\Rightarrow ( 2)^{( -16+12x)}\times( 2)^{( 3x-6)}=( 2)^{-2x}$
$\Rightarrow ( 2)^{( -16+12x+3x-6)}=( 2)^{-2x}$
$\Rightarrow ( 2)^{( 15x-22)}=( 2)^{-2x}$
$\Rightarrow 15x-22=-2x$
$\Rightarrow 15x+2x=22$
$\Rightarrow 17x=22$
$\Rightarrow x=\frac{22}{17}$
Therefore, $\frac{17x}{22}+1=\frac{17}{22}\times\frac{22}{17}+1$
$=1+1=2$
Thus, $\frac{17x}{22}+1=2$
Advertisements
To Continue Learning Please Login
Login with Google