When you see the same base on both sides, focus on the exponents because the exponential function is one-to-one. Here the bases are equal, so we set the exponents equal and solve the simple linear equation. Since the bases are equal and positive with base not equal to 1, set exponents equal: 2x+1=2. Hence x=(2-1)/2=1/2. Therefore, the correct value of x is the one that makes both exponents exactly the same.