Question

3125^{x+4} = 25^{2x}

Explanation:

Step1: Rewrite bases as powers of 5

$3125 = 5^5$, $25 = 5^2$, so:
$$5^{5(x+4)} = 5^{2(2x)}$$

Step2: Simplify exponents

$$5^{5x+20} = 5^{4x}$$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$5x + 20 = 4x$

Step4: Solve for x

Subtract $4x$ from both sides:
$x + 20 = 0$
Subtract 20 from both sides:
$x = -20$

Answer:

$x = -20$