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

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

A 0

B 1

C -1

D 4

Solution

Correct Answer: Option B

2 ^ a = 2(2) + a by definition of ^

a ^ 3 = 2(a) + 3 by definition of ^

Equate these two expressions:

2(2) + a = 2(a) + 3

Solve for a:

4 + a = 2a + 3

a = 1