Solve for x 3^x=1/3

$3^{x} = \frac{1}{3}$

Step 1

Raise $3$ to the power of $1$ .

$3^{x} = \frac{1}{3^{1}}$

Step 2

Move $3^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{x} = 3^{- 1}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = - 1$