Algebra Examples

$f (x) = 2^{2 x - 9} - 32$

Step 1

Set $2^{2 x - 9} - 32$ equal to $0$ .

$2^{2 x - 9} - 32 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $32$ to both sides of the equation.

$2^{2 x - 9} = 32$

Step 2.2

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

$2^{2 x - 9} = 2^{5}$

Step 2.3

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

$2 x - 9 = 5$

Step 2.4

Solve for $x$ .

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Step 2.4.1

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

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Step 2.4.1.1

Add $9$ to both sides of the equation.

$2 x = 5 + 9$

Step 2.4.1.2

Add $5$ and $9$ .

$2 x = 14$

Step 2.4.2

Divide each term in $2 x = 14$ by $2$ and simplify.

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Step 2.4.2.1

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $2$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Step 2.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Divide $14$ by $2$ .

$x = 7$

Step 3