Question

for x:
$4^{2x-4}=256^{2x-4}$
attempt 1 out of 2
submit answer

Explanation:

Step1: Rewrite base 256 as power of 4

$256 = 4^4$, so substitute into equation:
$4^{2x-4} = (4^4)^{2x-4}$

Step2: Simplify right-hand side exponent

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

Step3: Set exponents equal (same base)

Since $4^a=4^b$ implies $a=b$:
$2x - 4 = 4(2x - 4)$

Step4: Expand right-hand side

Distribute the 4:
$2x - 4 = 8x - 16$

Step5: Rearrange to solve for x

Subtract $2x$ and add 16 to both sides:
$-4 + 16 = 8x - 2x$
$12 = 6x$

Step6: Solve for x

Divide both sides by 6:
$x = \frac{12}{6} = 2$

Answer:

$x=2$