Multiple choice

If the operation,^ is defined by the equation x ^ y = 2x + y, what is the value of a in 2 ^ a = a ^ 3

  1. 0

  2. 1

  3. -1

  4. 4

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the definition x ^ y = 2x + y, evaluate both sides: 2 ^ a = 2(2) + a = 4 + a, and a ^ 3 = 2(a) + 3 = 2a + 3. Setting them equal: 4 + a = 2a + 3. Solving: 4 - 3 = 2a - a, so 1 = a. Verifying: 2 ^ 1 = 5 and 1 ^ 3 = 5, both equal.

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