Algebra Examples

$3^{2 x} = 9^{3 x - 4}$

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (3 x - 4)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply.

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Step 3.1.2.1

Multiply $3$ by $2$ .

$2 x = 6 x + 2 \cdot - 4$

Step 3.1.2.2

Multiply $2$ by $- 4$ .

$2 x = 6 x - 8$

Step 3.2

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

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Step 3.2.1

Subtract $6 x$ from both sides of the equation.

$2 x - 6 x = - 8$

Step 3.2.2

Subtract $6 x$ from $2 x$ .

$- 4 x = - 8$

Step 3.3

Divide each term in $- 4 x = - 8$ by $- 4$ and simplify.

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Step 3.3.1

Divide each term in $- 4 x = - 8$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 8}{- 4}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 4$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 8}{- 4}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 4}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 8$ by $- 4$ .

$x = 2$