Algebra Examples

$16^{3 x - 6} = 64^{x + 4}$

Step 1

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

$4^{2 (3 x - 6)} = 4^{3 (x + 4)}$

Step 2

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

$2 (3 x - 6) = 3 (x + 4)$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (3 x - 6)$ .

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Step 3.1.1

Rewrite.

$0 + 0 + 2 (3 x - 6) = 3 (x + 4)$

Step 3.1.2

Simplify by adding zeros.

$2 (3 x - 6) = 3 (x + 4)$

Step 3.1.3

Apply the distributive property.

$2 (3 x) + 2 \cdot - 6 = 3 (x + 4)$

Step 3.1.4

Multiply.

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Step 3.1.4.1

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 6 = 3 (x + 4)$

Step 3.1.4.2

Multiply $2$ by $- 6$ .

$6 x - 12 = 3 (x + 4)$

Step 3.2

Simplify $3 (x + 4)$ .

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Step 3.2.1

Apply the distributive property.

$6 x - 12 = 3 x + 3 \cdot 4$

Step 3.2.2

Multiply $3$ by $4$ .

$6 x - 12 = 3 x + 12$

Step 3.3

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

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Step 3.3.1

Subtract $3 x$ from both sides of the equation.

$6 x - 12 - 3 x = 12$

Step 3.3.2

Subtract $3 x$ from $6 x$ .

$3 x - 12 = 12$

Step 3.4

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

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Step 3.4.1

Add $12$ to both sides of the equation.

$3 x = 12 + 12$

Step 3.4.2

Add $12$ and $12$ .

$3 x = 24$

Step 3.5

Divide each term in $3 x = 24$ by $3$ and simplify.

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Step 3.5.1

Divide each term in $3 x = 24$ by $3$ .

$\frac{3 x}{3} = \frac{24}{3}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $3$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{24}{3}$

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{3}$

Step 3.5.3

Simplify the right side.

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Step 3.5.3.1

Divide $24$ by $3$ .

$x = 8$