If 2^(x+1) = 16, find x.

Explanation

• Write 16 as a power of 2: 16 = 2⁴, so the equation becomes 2^(x+1) = 2⁴.
• When the bases are the same, the exponents must be equal, so x + 1 = 4 and x = 3.
• Check by substituting back: 2^(3+1) = 2⁴ = 16, which matches the right side.
• Option C 4 is the usual trap, because 4 is the power of 2 that gives 16, but the exponent here is x + 1, not x.
• The same method solves any index equation of the form a^(x+k) = a^n: match the bases first, then equate the exponents.