Question

if (8^y = 16^{y+2}), what is the value of (y)?

-8
-4
-2
-1

Explanation:

⚡ Using what you learned: Solving Exponential Equations

Step 1: Rewrite with a common base

$$ 8^y = 16^{y+2} $$

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

Step 2: Apply exponent rules

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

$$ 3y = 4(y+2) $$

Step 3: Solve for y

$$ 3y = 4y + 8 $$

$$ -y = 8 $$

$$ y = -8 $$

Answer:

-8