If (\frac{2^{x+3}}{2^{x-1}}=16), what is the value of (x)?
Answer and explanation
Correct answer: Any real number
For division of powers with the same base, subtract the exponents: \(\frac{2^{x+3}}{2^{x-1}}=2^{(x+3)-(x-1)}=2^4=16\). Thus, the given equation is true for every real value of \(x\), so there is no single fixed value of \(x\). Therefore, option C is correct. Exam tip: use \(a^m/a^n=a^{m-n}\) for powers with the same non-zero base; here, \(x\) cancels out.
Frequently asked questions
What is the correct answer to this question?
Any real number
Why is this the correct answer?
For division of powers with the same base, subtract the exponents: \(\frac{2^{x+3}}{2^{x-1}}=2^{(x+3)-(x-1)}=2^4=16\). Thus, the given equation is true for every real value of \(x\), so there is no single fixed value of \(x\). Therefore, option C is correct. Exam tip: use \(a^m/a^n=a^{m-n}\) for powers with the same non-zero base; here, \(x\) cancels out.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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