Solve for x 2^(7-3x)=1/4

$2^{7 - 3 x} = \frac{1}{4}$

Step 1

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

$2^{7 - 3 x} = \frac{1}{4^{1}}$

Step 2

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

$2^{7 - 3 x} = 4^{- 1}$

Step 3

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

$2^{7 - 3 x} = 2^{- 2}$

Step 4

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

$7 - 3 x = - 2$

Step 5

Solve for $x$ .

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

Subtract $7$ from both sides of the equation.

$- 3 x = - 2 - 7$

Subtract $7$ from $- 2$ .

$- 3 x = - 9$

Divide each term in $- 3 x = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 9$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 9}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 9}{- 3}$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$x = 3$