Class 9 Exam > Class 9 Questions > 2^2x-5•2^5=256 then find the value of x.
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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.
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2^2x-5•2^5=256 then find the value of x.
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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..
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