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CORE SKILL ADVANCED: If 8^x = 8^y, which of the following is equal to y in terms of x?

(A) 8^x
(B) 8^(x+1)
(C) 8^(x-1)
(D) 8/x

User Rmmh
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1 Answer

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Final answer:

Since 8ˣ = 8ʸ, it must be that x equals y, due to the law of exponents which states that if aᵐ = aⁿ, then m = n. Thus, none of the provided options (A-D) are correct; the answer is simply x.

Step-by-step explanation:

The question asks us to solve for y in terms of x given that 8ˣ = 8ʸ. Since the bases are the same and the exponents must also be the same for the equality to hold, we can infer that y is equal to x.

To further explain, if we have an equation where the bases are the same (like 8 in this case), and since the only way for the entire expressions to be equal is if the powers are the same, it follows that x must be the same as y. This is based on the law of exponents which states that if aᵐ = aⁿ, then m = n as long as a is not zero.

Therefore, the correct answer is neither (A) 8ˣ, (B) 8ˣ⁺¹, (C) 8ˣ⁻¹, nor (D) 8/x, but simply x. Often, these type of questions seek to test understanding of exponential functions and their properties.

User Grumbler
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