Question

solve. write your answer as an integer or a fraction in simplest form.
\\(\frac{1}{9} = 9^x\\)
\\(x = \\)

Explanation:

Step1: Rewrite 1/9 as a power of 9

We know that \( \frac{1}{9} = 9^{-1} \) because \( 9^1 = 9 \) and a negative exponent indicates the reciprocal, so \( 9^{-1}=\frac{1}{9^1}=\frac{1}{9} \).

Step2: Set the exponents equal

Now we have the equation \( 9^{-1}=9^{x} \). Since the bases are the same (both are 9) and the equation holds, the exponents must be equal. So we can set \( -1 = x \).

Answer:

\( -1 \)