Algebra Examples

$2^{x - 1} + 2^{x - 2} + 2^{x - 3} + 2^{x - 4} = 960$

Step 1

Factor out $2^{x - 4}$ from the expression.

$2^{x - 4} (8 + 4 + 2 + 1)$

Step 2

Add $8$ and $4$ .

$2^{x - 4} (12 + 2 + 1) = 960$

Step 3

Add $12$ and $2$ .

$2^{x - 4} (14 + 1) = 960$

Step 4

Add $14$ and $1$ .

$2^{x - 4} \cdot 15 = 960$

Step 5

Move $15$ to the left of $2^{x - 4}$ .

$15 \cdot 2^{x - 4} = 960$

Step 6

Divide each term in $15 \cdot 2^{x - 4} = 960$ by $15$ and simplify.

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Step 6.1

Divide each term in $15 \cdot 2^{x - 4} = 960$ by $15$ .

$\frac{15 \cdot 2^{x - 4}}{15} = \frac{960}{15}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $15$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{15 \cdot 2^{x - 4}}{15} = \frac{960}{15}$

Step 6.2.1.2

Divide $2^{x - 4}$ by $1$ .

$2^{x - 4} = \frac{960}{15}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $960$ by $15$ .

$2^{x - 4} = 64$

Step 7

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

$2^{x - 4} = 2^{6}$

Step 8

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

$x - 4 = 6$

Step 9

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

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Step 9.1

Add $4$ to both sides of the equation.

$x = 6 + 4$

Step 9.2

Add $6$ and $4$ .

$x = 10$