Algebra Examples

$4 (3^{- 2 x - 4}) = 36$

Step 1

Divide each term in $4 \cdot 3^{- 2 x - 4} = 36$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 \cdot 3^{- 2 x - 4} = 36$ by $4$ .

$\frac{4 \cdot 3^{- 2 x - 4}}{4} = \frac{36}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 \cdot 3^{- 2 x - 4}}{4} = \frac{36}{4}$

Step 1.2.1.2

Divide $3^{- 2 x - 4}$ by $1$ .

$3^{- 2 x - 4} = \frac{36}{4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $36$ by $4$ .

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

Step 2

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

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

Step 3

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

$- 2 x - 4 = 2$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $4$ to both sides of the equation.

$- 2 x = 2 + 4$

Step 4.1.2

Add $2$ and $4$ .

$- 2 x = 6$

Step 4.2

Divide each term in $- 2 x = 6$ by $- 2$ and simplify.

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Step 4.2.1

Divide each term in $- 2 x = 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{- 2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $6$ by $- 2$ .

$x = - 3$