Finite Math Examples

$16^{x + 4} = 64^{3 x - 7}$

Step 1

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

$4^{2 (x + 4)} = 4^{3 (3 x - 7)}$

Step 2

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

$2 (x + 4) = 3 (3 x - 7)$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (x + 4)$ .

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Step 3.1.1

Rewrite.

$0 + 0 + 2 (x + 4) = 3 (3 x - 7)$

Step 3.1.2

Simplify by adding zeros.

$2 (x + 4) = 3 (3 x - 7)$

Step 3.1.3

Apply the distributive property.

$2 x + 2 \cdot 4 = 3 (3 x - 7)$

Step 3.1.4

Multiply $2$ by $4$ .

$2 x + 8 = 3 (3 x - 7)$

Step 3.2

Simplify $3 (3 x - 7)$ .

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Step 3.2.1

Apply the distributive property.

$2 x + 8 = 3 (3 x) + 3 \cdot - 7$

Step 3.2.2

Multiply.

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Step 3.2.2.1

Multiply $3$ by $3$ .

$2 x + 8 = 9 x + 3 \cdot - 7$

Step 3.2.2.2

Multiply $3$ by $- 7$ .

$2 x + 8 = 9 x - 21$

Step 3.3

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

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Step 3.3.1

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

$2 x + 8 - 9 x = - 21$

Step 3.3.2

Subtract $9 x$ from $2 x$ .

$- 7 x + 8 = - 21$

Step 3.4

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

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Step 3.4.1

Subtract $8$ from both sides of the equation.

$- 7 x = - 21 - 8$

Step 3.4.2

Subtract $8$ from $- 21$ .

$- 7 x = - 29$

Step 3.5

Divide each term in $- 7 x = - 29$ by $- 7$ and simplify.

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Step 3.5.1

Divide each term in $- 7 x = - 29$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 29}{- 7}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $- 7$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 29}{- 7}$

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 29}{- 7}$

Step 3.5.3

Simplify the right side.

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Step 3.5.3.1

Dividing two negative values results in a positive value.

$x = \frac{29}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{29}{7}$

Decimal Form:

$x = 4.\overline{142857}$

Mixed Number Form:

$x = 4 \frac{1}{7}$