Algebra Examples

$4^{x + 1} + 4^{x} = 160$

Step 1

Factor out $4^{x}$ from the expression.

$4^{x} (4 + 1)$

Step 2

Add $4$ and $1$ .

$4^{x} \cdot 5 = 160$

Step 3

Move $5$ to the left of $4^{x}$ .

$5 \cdot 4^{x} = 160$

Step 4

Divide each term in $5 \cdot 4^{x} = 160$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 \cdot 4^{x} = 160$ by $5$ .

$\frac{5 \cdot 4^{x}}{5} = \frac{160}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 \cdot 4^{x}}{5} = \frac{160}{5}$

Step 4.2.1.2

Divide $4^{x}$ by $1$ .

$4^{x} = \frac{160}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $160$ by $5$ .

$4^{x} = 32$

Step 5

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

$2^{2 x} = 2^{5}$

Step 6

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

$2 x = 5$

Step 7

Divide each term in $2 x = 5$ by $2$ and simplify.

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Step 7.1

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $2$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

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