Class 11 Exam > Class 11 Questions > 1/(2^x - 1) > 1/(1- 2^(x-1)) please solve?
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1/(2^x - 1) > 1/(1- 2^(x-1)) please solve?
Most Upvoted Answer
1/(2^x - 1) > 1/(1- 2^(x-1)) please solve?
1/(2^x-1)>1/(1-2(x-1)),
or, 1-2(x-1)>2^x-1,
2>2^(2x-1),
by comparing the powers,
1>2x-1,
2>2x,
1>x
or, 1-2(x-1)>2^x-1,
2>2^(2x-1),
by comparing the powers,
1>2x-1,
2>2x,
1>x
Community Answer
1/(2^x - 1) > 1/(1- 2^(x-1)) please solve?
Step 1: Understand the Inequality
We need to solve the inequality:
1/(2^x - 1) > 1/(1 - 2^(x-1))
This can be rewritten to make it easier to analyze.
Step 2: Cross-Multiply
Cross-multiplying gives us:
1 * (1 - 2^(x-1)) > 1 * (2^x - 1)
This simplifies to:
1 - 2^(x-1) > 2^x - 1
Step 3: Rearrange the Terms
Rearranging the inequality, we get:
1 + 1 > 2^x + 2^(x-1)
This simplifies to:
2 > 2^x + 2^(x-1)
Step 4: Factor the Right Side
Notice that 2^(x-1) can be factored out:
2 > 2^(x-1) * (2 + 1)
This simplifies to:
2 > 2^(x-1) * 3
Step 5: Divide Both Sides
Dividing both sides by 3 (valid since 3 is positive):
2/3 > 2^(x-1)
Step 6: Solve for x
Taking logarithms, we convert the inequality:
x - 1 < />
Thus:
x < log2(2/3)="" +="" />
Step 7: Conclusion
- The solution to the inequality is:
x < log2(2/3)="" +="" />
This highlights the values of x that satisfy the original inequality.
We need to solve the inequality:
1/(2^x - 1) > 1/(1 - 2^(x-1))
This can be rewritten to make it easier to analyze.
Step 2: Cross-Multiply
Cross-multiplying gives us:
1 * (1 - 2^(x-1)) > 1 * (2^x - 1)
This simplifies to:
1 - 2^(x-1) > 2^x - 1
Step 3: Rearrange the Terms
Rearranging the inequality, we get:
1 + 1 > 2^x + 2^(x-1)
This simplifies to:
2 > 2^x + 2^(x-1)
Step 4: Factor the Right Side
Notice that 2^(x-1) can be factored out:
2 > 2^(x-1) * (2 + 1)
This simplifies to:
2 > 2^(x-1) * 3
Step 5: Divide Both Sides
Dividing both sides by 3 (valid since 3 is positive):
2/3 > 2^(x-1)
Step 6: Solve for x
Taking logarithms, we convert the inequality:
x - 1 < />
Thus:
x < log2(2/3)="" +="" />
Step 7: Conclusion
- The solution to the inequality is:
x < log2(2/3)="" +="" />
This highlights the values of x that satisfy the original inequality.
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1/(2^x - 1) > 1/(1- 2^(x-1)) please solve?
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1/(2^x - 1) > 1/(1- 2^(x-1)) please solve? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 1/(2^x - 1) > 1/(1- 2^(x-1)) please solve? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1/(2^x - 1) > 1/(1- 2^(x-1)) please solve?.
1/(2^x - 1) > 1/(1- 2^(x-1)) please solve? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 1/(2^x - 1) > 1/(1- 2^(x-1)) please solve? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1/(2^x - 1) > 1/(1- 2^(x-1)) please solve?.
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