Finite Math Examples

$7^{- 3} = 49^{x + 3}$

Step 1

Rewrite the equation as $49^{x + 3} = 7^{- 3}$ .

$49^{x + 3} = 7^{- 3}$

Step 2

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

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

Step 3

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

$2 (x + 3) = - 3$

Step 4

Solve for $x$ .

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Step 4.1

Divide each term in $2 (x + 3) = - 3$ by $2$ and simplify.

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Step 4.1.1

Divide each term in $2 (x + 3) = - 3$ by $2$ .

$\frac{2 (x + 3)}{2} = \frac{- 3}{2}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $2$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{2 (x + 3)}{2} = \frac{- 3}{2}$

Step 4.1.2.1.2

Divide $x + 3$ by $1$ .

$x + 3 = \frac{- 3}{2}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Move the negative in front of the fraction.

$x + 3 = - \frac{3}{2}$

Step 4.2

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

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$x = - \frac{3}{2} - 3$

Step 4.2.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{3}{2} - 3 \cdot \frac{2}{2}$

Step 4.2.3

Combine $- 3$ and $\frac{2}{2}$ .

$x = - \frac{3}{2} + \frac{- 3 \cdot 2}{2}$

Step 4.2.4

Combine the numerators over the common denominator.

$x = \frac{- 3 - 3 \cdot 2}{2}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 3$ by $2$ .

$x = \frac{- 3 - 6}{2}$

Step 4.2.5.2

Subtract $6$ from $- 3$ .

$x = \frac{- 9}{2}$

Step 4.2.6

Move the negative in front of the fraction.

$x = - \frac{9}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{9}{2}$

Decimal Form:

$x = - 4.5$

Mixed Number Form:

$x = - 4 \frac{1}{2}$