Algebra Examples

$9^{x - 6} = 729^{3 (x + 2)}$

Step 1

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

$9^{x - 6} = 9^{3 (3 (x + 2))}$

Step 2

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

$x - 6 = 3 (3 (x + 2))$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $3 \cdot (3 (x + 2))$ .

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Step 3.1.1

Rewrite.

$x - 6 = 0 + 0 + 3 \cdot (3 (x + 2))$

Step 3.1.2

Simplify by adding zeros.

$x - 6 = 3 \cdot (3 (x + 2))$

Step 3.1.3

Apply the distributive property.

$x - 6 = 3 \cdot (3 x + 3 \cdot 2)$

Step 3.1.4

Multiply $3$ by $2$ .

$x - 6 = 3 \cdot (3 x + 6)$

Step 3.1.5

Apply the distributive property.

$x - 6 = 3 (3 x) + 3 \cdot 6$

Step 3.1.6

Multiply.

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Step 3.1.6.1

Multiply $3$ by $3$ .

$x - 6 = 9 x + 3 \cdot 6$

Step 3.1.6.2

Multiply $3$ by $6$ .

$x - 6 = 9 x + 18$

Step 3.2

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

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Step 3.2.1

Subtract $9 x$ from both sides of the equation.

$x - 6 - 9 x = 18$

Step 3.2.2

Subtract $9 x$ from $x$ .

$- 8 x - 6 = 18$

Step 3.3

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

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Step 3.3.1

Add $6$ to both sides of the equation.

$- 8 x = 18 + 6$

Step 3.3.2

Add $18$ and $6$ .

$- 8 x = 24$

Step 3.4

Divide each term in $- 8 x = 24$ by $- 8$ and simplify.

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Step 3.4.1

Divide each term in $- 8 x = 24$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $- 8$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{- 8}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $24$ by $- 8$ .

$x = - 3$