If 9^x = 729 and 27^y = 729, what is the value of x + y?
Answer and explanation
Correct answer: 5
Express all quantities with the common base 3. Since 729 = 3^6 and 9 = 3^2, the first equation becomes (3^2)^x = 3^(2x) = 3^6, so 2x = 6 and x = 3. Since 27 = 3^3, the second equation becomes (3^3)^y = 3^(3y) = 3^6, giving 3y = 6 and y = 2. Consequently, x + y = 3 + 2 = 5. Therefore option C is the correct answer. Option A is the value of x+y if the bases are mishandled, while 9/2 and 6 do not satisfy the two exponent equations.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Express all quantities with the common base 3. Since 729 = 3^6 and 9 = 3^2, the first equation becomes (3^2)^x = 3^(2x) = 3^6, so 2x = 6 and x = 3. Since 27 = 3^3, the second equation becomes (3^3)^y = 3^(3y) = 3^6, giving 3y = 6 and y = 2. Consequently, x + y = 3 + 2 = 5. Therefore option C is the correct answer. Option A is the value of x+y if the bases are mishandled, while 9/2 and 6 do not satisfy the two exponent equations.
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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