Multiple choice

Solve the equation: $2^{2x+3}=32.2^x$

  1. $-4$
  2. $4$
  3. $2$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

2^(2x+3) = 32 * 2^x. Since 32 = 2^5, the equation is 2^(2x+3) = 2^5 * 2^x = 2^(x+5). Equating exponents: 2x + 3 = x + 5, so x = 2.

AI explanation

Expressing 32 as a power of 2 gives the equation 2^(2x+3) = 2^5 * 2^x. Using the laws of exponents, the right side simplifies to 2^(x+5). Since the bases are identical, we can equate the exponents to get 2x + 3 = x + 5. Solving this linear equation yields x = 2.

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