Evaluate (1/27)^(4-x)=9^(2x-1)

${(\frac{1}{27})}^{4 - x} = 9^{2 x - 1}$

Step 1

Apply the product rule to $\frac{1}{27}$ .

$\frac{1^{4 - x}}{27^{4 - x}} = 9^{2 x - 1}$

Step 2

One to any power is one.

$\frac{1}{27^{4 - x}} = 9^{2 x - 1}$

Step 3

Move $27^{4 - x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$27^{- (4 - x)} = 9^{2 x - 1}$

Step 4

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

$3^{3 (- (4 - x))} = 3^{2 (2 x - 1)}$

Step 5

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

$3 (- (4 - x)) = 2 (2 x - 1)$

Step 6

Solve for $x$ .

Simplify $3 (- (4 - x))$ .

Start simplifying.

$0 + 0 + 3 (- (4 - x)) = 2 (2 x - 1)$

Simplify by adding zeros.

$3 (- (4 - x)) = 2 (2 x - 1)$

Apply the distributive property.

$3 (- 1 \cdot 4 - - x) = 2 (2 x - 1)$

Multiply $- 1$ by $4$ .

$3 (- 4 - - x) = 2 (2 x - 1)$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$3 (- 4 + 1 x) = 2 (2 x - 1)$

Multiply $x$ by $1$ .

$3 (- 4 + x) = 2 (2 x - 1)$

Apply the distributive property.

$3 \cdot - 4 + 3 x = 2 (2 x - 1)$

Multiply $3$ by $- 4$ .

$- 12 + 3 x = 2 (2 x - 1)$

Simplify $2 (2 x - 1)$ .

Apply the distributive property.

$- 12 + 3 x = 2 (2 x) + 2 \cdot - 1$

Multiply.

Multiply $2$ by $2$ .

$- 12 + 3 x = 4 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$- 12 + 3 x = 4 x - 2$

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$- 12 + 3 x - 4 x = - 2$

Subtract $4 x$ from $3 x$ .

$- 12 - x = - 2$

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

Add $12$ to both sides of the equation.

$- x = - 2 + 12$

Add $- 2$ and $12$ .

$- x = 10$

Divide each term in $- x = 10$ by $- 1$ and simplify.

Divide each term in $- x = 10$ by $- 1$ .

$\frac{- x}{- 1} = \frac{10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{10}{- 1}$

Divide $x$ by $1$ .

$x = \frac{10}{- 1}$

Simplify the right side.

Divide $10$ by $- 1$ .

$x = - 10$

Evaluate (1/27)^(4-x)=9^(2x-1)

Related Questions

Support LCMGCF.com by disabling your adblocker.