Solve for x 3^(1-x)=1/27

$3^{1 - x} = \frac{1}{27}$

Step 1

Raise $27$ to the power of $1$ .

$3^{1 - x} = \frac{1}{27^{1}}$

Step 2

Move $27^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{1 - x} = 27^{- 1}$

Step 3

Create equivalent expressions in the equation that all have equal bases.

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

Step 4

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

$1 - x = - 3$

Step 5

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$- x = - 3 - 1$

Subtract $1$ from $- 3$ .

$- x = - 4$

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x = 4$