Question

question
solve for x:
$256^{3x + 5} = 16^4$

Explanation:

Step1: Rewrite bases as powers of 2

$256 = 2^8$, $16 = 2^4$, so substitute:
$$(2^8)^{3x+5} = (2^4)^4$$

Step2: Simplify exponents via power rule

Power rule: $(a^m)^n=a^{m \cdot n}$. Calculate:
$$2^{8(3x+5)} = 2^{16}$$

Step3: Set exponents equal (same base)

Since bases are equal, exponents match:
$$8(3x+5) = 16$$

Step4: Divide both sides by 8

Isolate the parenthetical term:
$$3x+5 = \frac{16}{8} = 2$$

Step5: Subtract 5 from both sides

Isolate the $x$-term:
$$3x = 2 - 5 = -3$$

Step6: Solve for x by dividing by 3

Divide to get final $x$ value:
$$x = \frac{-3}{3} = -1$$

Answer:

$x = -1$