for what value of x does 625 = 5^{6 - 2x}?\n1\n2\n4\n5

Explanation:

Step1: Rewrite 625 as a power of 5

Since $625 = 5^4$, the equation becomes $5^4=5^{6 - 2x}$.

Step2: Set the exponents equal

If $a^m=a^n$, then $m = n$. So, $4=6 - 2x$.

Step3: Solve for x

First, subtract 6 from both sides: $4-6=-2x$, which simplifies to $-2=-2x$. Then divide both sides by - 2: $x = 1$.

Answer:

1