Solve for x 4^(1-x)=1/4

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

Step 1

Raise $4$ to the power of $1$ .

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

Step 2

Move $4^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$4^{1 - x} = 4^{- 1}$

Step 3

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

$1 - x = - 1$

Step 4

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$- x = - 1 - 1$

Subtract $1$ from $- 1$ .

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$