if (3^{2x + 1}=3^{x + 5}), what is the value of (x)?\n2\n3\n4\n6

Explanation:

Step1: Apply exponential - equality rule

If (a^m=a^n), then (m = n). Here (a = 3), (m=2x + 1), and (n=x + 5). So we get the equation (2x+1=x + 5).

Step2: Solve the linear equation

Subtract (x) from both sides: (2x - x+1=x - x + 5), which simplifies to (x+1 = 5).

Step3: Isolate (x)

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

Answer:

4