Question

algebra: concepts and connections - plc solving exponential equations by rewriting the base if $8^y = 16^{y + 2}$, what is the value of $y$? -8 -2 -4 -1

Explanation:

Step1: Rewrite bases as powers of 2

$8^y = (2^3)^y = 2^{3y}$, $16^{y+2} = (2^4)^{y+2} = 2^{4(y+2)}$

Step2: Set exponents equal

$3y = 4(y+2)$

Step3: Expand right-hand side

$3y = 4y + 8$

Step4: Solve for y

$3y - 4y = 8 \implies -y = 8 \implies y = -8$

Answer:

$-8$