Question

question
solve for x:
$256^{x + 5} = 64^{2x + 4}$
answer
attempt 1 out of 2
$x = \square$ submit answer

Explanation:

Step1: Express bases as powers of 2

$256 = 2^8$, $64 = 2^6$, so rewrite the equation:
$$(2^8)^{x+5} = (2^6)^{2x+4}$$

Step2: Simplify exponents

Use exponent rule $(a^m)^n=a^{m \cdot n}$:
$$2^{8(x+5)} = 2^{6(2x+4)}$$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$$8(x+5) = 6(2x+4)$$

Step4: Expand both sides

$$8x + 40 = 12x + 24$$

Step5: Isolate x terms

Subtract $8x$ and $24$ from both sides:
$$40 - 24 = 12x - 8x$$
$$16 = 4x$$

Step6: Solve for x

Divide both sides by 4:
$$x = \frac{16}{4}$$

Answer:

$x = 4$