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If (16^{x}=1024) and (32^{y}=1024), what is the value of (x+y)?
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Answer and explanation
Correct answer: (\frac{9}{2})
Since (1024=2^{10}), (16^{x}=2^{4x}) gives (x=\frac{5}{2}), and (32^{y}=2^{5y}) gives (y=2). Hence the sum is (\frac{9}{2}).
Frequently asked questions
What is the correct answer to this question?
(\frac{9}{2})
Why is this the correct answer?
Since (1024=2^{10}), (16^{x}=2^{4x}) gives (x=\frac{5}{2}), and (32^{y}=2^{5y}) gives (y=2). Hence the sum is (\frac{9}{2}).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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