if (5^{3b - 1}=5^{b - 3}), what is the value of (b)?\n-2\n-1\n1\n2

Explanation:

Step1: Use exponential - equality rule

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

Step2: Isolate the variable (b) terms

Subtract (b) from both sides: (3b - 1-b=b - 3-b), which simplifies to (2b-1=-3).

Step3: Isolate the variable (b) further

Add 1 to both sides: (2b-1 + 1=-3 + 1), getting (2b=-2).

Step4: Solve for (b)

Divide both sides by 2: (\frac{2b}{2}=\frac{-2}{2}), so (b=-1).

Answer:

B. -1