Question

solve. write your answer as an integer or a fraction in simplest form.
\\(\frac{1}{3} = 3^x\\)
\\(x = \boxed{}\\)

Explanation:

Step1: Rewrite the left side

We know that $\frac{1}{3}$ can be written as $3^{-1}$ because a negative exponent means the reciprocal, so $a^{-n}=\frac{1}{a^{n}}$. So we have $3^{-1}=3^{x}$.

Step2: Use the property of exponents

If two exponential expressions with the same base are equal, then their exponents must be equal. That is, if $b^{m}=b^{n}$, then $m = n$ (where $b>0,b
eq1$). Here, the base $b = 3$, so we can set the exponents equal: $- 1=x$.

Answer:

$-1$