Question

$16^{2x - 3} = 8^{3x + 4}$

Explanation:

Step1: Rewrite bases as powers of 2

$16=2^4$, $8=2^3$, so substitute:
$2^{4(2x-3)} = 2^{3(3x+4)}$

Step2: Set exponents equal

Since bases are equal, exponents match:
$4(2x-3) = 3(3x+4)$

Step3: Expand both sides

Calculate products on each side:
$8x - 12 = 9x + 12$

Step4: Isolate x variable

Subtract $8x$ and 12 from both sides:
$-12 - 12 = 9x - 8x$

Step5: Solve for x

Simplify to find x:
$x = -24$

Answer:

$x=-24$