27^x=1/3

To solve the equation \( 27^x = \frac{1}{3} \), we can first express both sides of the equation with the same base.

We know that \( 27 \) can be written as \( 3^3 \), so we can rewrite the left side of the equation:

\[ 27^x = (3^3)^x = 3^{3x} \]

Now, our equation looks like this:

\[ 3^{3x} = \frac{1}{3} \]

Next, we can express \( \frac{1}{3} \) as a power of \( 3 \):

\[ \frac{1}{3} = 3^{-1} \]

So the equation becomes:

\[ 3^{3x} = 3^{-1} \]

Since the bases are the same, we can set the exponents equal to each other:

\[ 3x = -1 \]

Now, we solve for \( x \):

\[ x = \frac{-1}{3} \]

Thus, the solution to the equation \( 27^x = \frac{1}{3} \) is:

\[ \boxed{-\frac{1}{3}} \]