Question

question
solve for x:
$256^{2x - 4} = 1024^{x - 5}$
answer
attempt 1 out of 2
$x = $

Explanation:

Step1: Rewrite bases as powers of 2

$256 = 2^8$, $1024 = 2^{10}$, so:
$$(2^8)^{2x-4} = (2^{10})^{x-5}$$

Step2: Simplify exponents

Use exponent rule $(a^m)^n=a^{m \cdot n}$:
$$2^{8(2x-4)} = 2^{10(x-5)}$$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$$8(2x-4) = 10(x-5)$$

Step4: Expand both sides

$$16x - 32 = 10x - 50$$

Step5: Isolate x terms

Subtract $10x$ from both sides:
$$6x - 32 = -50$$

Step6: Solve for x

Add 32 to both sides, then divide by 6:
$$6x = -18 \implies x = \frac{-18}{6} = -3$$

Answer:

$x = -3$