Solve for x 4^(5-9x)=1/(8^(x-2))

$4^{5 - 9 x} = \frac{1}{8^{x - 2}}$

Step 1

Move $8^{x - 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{5 - 9 x} = 8^{- (x - 2)}$

Step 2

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

$2^{2 (5 - 9 x)} = 2^{3 (- (x - 2))}$

Step 3

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

$2 (5 - 9 x) = 3 (- (x - 2))$

Step 4

Solve for $x$ .

Simplify $2 (5 - 9 x)$ .

Start simplifying.

$0 + 0 + 2 (5 - 9 x) = 3 (- (x - 2))$

Simplify by adding zeros.

$2 (5 - 9 x) = 3 (- (x - 2))$

Apply the distributive property.

$2 \cdot 5 + 2 (- 9 x) = 3 (- (x - 2))$

Multiply.

Multiply $2$ by $5$ .

$10 + 2 (- 9 x) = 3 (- (x - 2))$

Multiply $- 9$ by $2$ .

$10 - 18 x = 3 (- (x - 2))$

Simplify $3 (- (x - 2))$ .

Apply the distributive property.

$10 - 18 x = 3 (- x - - 2)$

Multiply $- 1$ by $- 2$ .

$10 - 18 x = 3 (- x + 2)$

Apply the distributive property.

$10 - 18 x = 3 (- x) + 3 \cdot 2$

Multiply.

Multiply $- 1$ by $3$ .

$10 - 18 x = - 3 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$10 - 18 x = - 3 x + 6$

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

Add $3 x$ to both sides of the equation.

$10 - 18 x + 3 x = 6$

Add $- 18 x$ and $3 x$ .

$10 - 15 x = 6$

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

Subtract $10$ from both sides of the equation.

$- 15 x = 6 - 10$

Subtract $10$ from $6$ .

$- 15 x = - 4$

Divide each term in $- 15 x = - 4$ by $- 15$ and simplify.

Divide each term in $- 15 x = - 4$ by $- 15$ .

$\frac{- 15 x}{- 15} = \frac{- 4}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} = \frac{- 4}{- 15}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 15}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{4}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{15}$

Decimal Form:

$x = 0.2\overline{6}$

Solve for x 4^(5-9x)=1/(8^(x-2))

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