If 5 Superscript x Baseline equals StartFraction 1 over 25 EndFraction, what is the value of x?

Question

Answer options with 5 options
A.
negative 2

B.
negative 1

C.
negative 1-half

D.
1-half

E.
2

Answer 1

To solve the equation \( 5^x = \frac{1}{25} \), we can first rewrite \( \frac{1}{25} \) as a power of 5.

We know that: \[ 25 = 5^2 \] Thus: \[ \frac{1}{25} = 5^{-2} \]

Now we can rewrite the original equation: \[ 5^x = 5^{-2} \]

Since the bases are the same, we can set the exponents equal to each other: \[ x = -2 \]

Thus, the value of \( x \) is \( \boxed{-2} \).

So the correct answer is option A: negative 2.