Question

question
solve for x:
$16^{2x + 3} = 2^{3x + 2}$
answer attempt 1 out of 2
$x = \square$

Explanation:

Step1: Rewrite base 16 as power of 2

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

Step2: Set exponents equal (same base)

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

Step3: Expand left-hand side

Distribute the 4:
$8x + 12 = 3x + 2$

Step4: Isolate x terms

Subtract $3x$ from both sides:
$5x + 12 = 2$

Step5: Isolate constant terms

Subtract 12 from both sides:
$5x = -10$

Step6: Solve for x

Divide both sides by 5:
$x = \frac{-10}{5}$

Answer:

$x = -2$