Question

algebra: concepts and connections - plc solving exponential equations by rewriting the base if ( 5^{3b - 1} = 5^{b - 3} ), what is the value of ( b )? options: ( -2 ), ( 2 ), ( -1 ), ( 1 )

Explanation:

Step1: Set exponents equal

Since bases are equal ($5=5$), we equate exponents:
$3b - 1 = b - 3$

Step2: Isolate $b$ terms

Subtract $b$ from both sides:
$3b - b - 1 = -3$
$2b - 1 = -3$

Step3: Solve for $b$

Add 1 to both sides, then divide by 2:
$2b = -3 + 1$
$2b = -2$
$b = \frac{-2}{2} = -1$

Answer:

$-1$