Algebra Examples

$\sqrt{5} = 5^{x + 4}$

Step 1

Rewrite the equation as $5^{x + 4} = \sqrt{5}$ .

$5^{x + 4} = \sqrt{5}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$5^{x + 4} = 5^{\frac{1}{2}}$

Step 3

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

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

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

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

Step 4.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.3

Combine $- 4$ and $\frac{2}{2}$ .

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 4$ by $2$ .

$x = \frac{1 - 8}{2}$

Step 4.5.2

Subtract $8$ from $1$ .

$x = \frac{- 7}{2}$

Step 4.6

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{2}$

Decimal Form:

$x = - 3.5$

Mixed Number Form:

$x = - 3 \frac{1}{2}$