solve: 3,125 = 5^{-10 + 3x}\nx = \ndone

Explanation:

Step1: Simplify the right - hand side exponent

First, simplify the exponent in the equation $3125 = 5^{- 10 + 3x}$. We know that $3125=5^5$ and the right - hand side is $5^{-10 + 3x}$. So the equation becomes $5^5=5^{-10 + 3x}$.

Step2: Set exponents equal

Since the bases are the same (both are 5), we can set the exponents equal to each other. So we have the equation $5=-10 + 3x$.

Step3: Solve for x

Add 10 to both sides of the equation $5=-10 + 3x$: $5+10=-10 + 3x+10$, which simplifies to $15 = 3x$. Then divide both sides by 3: $\frac{15}{3}=\frac{3x}{3}$, so $x = 5$.

Answer:

$5$