If \(2^{x+1}=32\), what is the value of \(x\)?

Correct answer: 4

The governing concept is equality of powers with the same positive base. Express 32 as a power of 2: \(32=2^5\). The equation therefore becomes \(2^{x+1}=2^5\). Since the base 2 is the same on both sides and is not 0 or 1, the exponents must be equal, giving \(x+1=5\). Subtracting 1 from both sides yields \(x=4\). Substitution confirms the result: \(2^{4+1}=2^5=32\). Thus option A is correct. Option B gives the exponent \(x+1\), not \(x\); option C results from subtracting incorrectly, and option D adds rather than subtracts 1.