Which one is the solution of 9^(2x + 2) = 25^(x + 1)?

Correct answer: c −1

9^(2x+2) = 81^(x+1) and 81 ≠ 25, so the exponent is zero: x + 1 = 0, x = −1.

Why the other options are wrong

• a −3: For x = −3 we get 9⁻⁴ ≠ 25⁻²; when the bases differ the exponent must be 0: x + 1 = 0.
• b −2: For x = −2 we get 9⁻² ≠ 25⁻¹; the right solution is x + 1 = 0.
• d 2: For x = 2 we get 9⁶ ≠ 25³; the right solution is x = −1.