Class 9 Exam > Class 9 Questions > 2^2x-5•2^5=256 then find the value of x.
Start Learning for Free
2^2x-5•2^5=256 then find the value of x.
Most Upvoted Answer
2^2x-5•2^5=256 then find the value of x.
Solution:
Step 1: Simplify the equation
Using the laws of exponents, we can simplify the left side of the equation as follows:
2^(2x) - 5•2^5 = 256
2^(2x) - 160 = 256
2^(2x) = 416
Step 2: Write 416 as a power of 2
Since 416 is not a power of 2, we can write it as a product of powers of 2:
416 = 2^6 • 6.5
Step 3: Substitute 416 as a power of 2 in the equation
Substituting 416 as a power of 2 in the equation, we get:
2^(2x) = 2^6 • 6.5
2^(2x) = 2^6 • 2^log2(6.5)
2^(2x) = 2^(6 + log2(6.5))
Step 4: Equate the exponents
Since the bases are the same, we can equate the exponents:
2x = 6 + log2(6.5)
Step 5: Solve for x
Solving for x, we get:
x = (6 + log2(6.5))/2
x ≈ 3.21
Step 6: Check the solution
To check the solution, we substitute x = 3.21 in the original equation:
2^(2x) - 5•2^5 = 256
2^(2•3.21) - 5•2^5 ≈ 256
416 - 160 ≈ 256
256 ≈ 256
Therefore, the solution is correct.
Final Answer:
The value of x is approximately 3.21.
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
2^2x-5•2^5=256 then find the value of x.
Question Description
2^2x-5•2^5=256 then find the value of x. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 2^2x-5•2^5=256 then find the value of x. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2^2x-5•2^5=256 then find the value of x..
2^2x-5•2^5=256 then find the value of x. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 2^2x-5•2^5=256 then find the value of x. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2^2x-5•2^5=256 then find the value of x..
Solutions for 2^2x-5•2^5=256 then find the value of x. in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of 2^2x-5•2^5=256 then find the value of x. defined & explained in the simplest way possible. Besides giving the explanation of
2^2x-5•2^5=256 then find the value of x., a detailed solution for 2^2x-5•2^5=256 then find the value of x. has been provided alongside types of 2^2x-5•2^5=256 then find the value of x. theory, EduRev gives you an
ample number of questions to practice 2^2x-5•2^5=256 then find the value of x. tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup