what is the solution to the equation ( 2^{x + 4}-12 = 20 )?\n( x = 0 )\n( x = 1 )\n( x = 2 )\n( x = 9 )

Explanation:

Step1: Isolate the exponential term

Add (12) to both sides of the equation (2^{x + 4}-12 = 20). (2^{x+4}-12 + 12=20 + 12) (2^{x + 4}=32)

Step2: Rewrite (32) as a power of (2)

Since (32 = 2^5), the equation becomes (2^{x + 4}=2^5).

Step3: Use the property of exponents

If (a^m=a^n), then (m = n). So, (x + 4=5).

Step4: Solve for (x)

Subtract (4) from both sides: (x+4 - 4=5 - 4) (x = 1)

Answer:

(x = 1) (the second option)