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If (4^{x+1}=64^{x-1}), then (x=)?
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Answer and explanation
Correct answer: 2
Express 4 and 64 as powers of 2: \(4^{x+1}=2^{2x+2}\) and \(64^{x-1}=2^{6x-6}\). Since the bases are equal, equate the exponents: \(2x+2=6x-6\). Thus, \(8=4x\), giving \(x=2\). Exam tip: When an exponential equation is reduced to the same base, equate the exponents.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Express 4 and 64 as powers of 2: \(4^{x+1}=2^{2x+2}\) and \(64^{x-1}=2^{6x-6}\). Since the bases are equal, equate the exponents: \(2x+2=6x-6\). Thus, \(8=4x\), giving \(x=2\). Exam tip: When an exponential equation is reduced to the same base, equate the exponents.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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