Algebra Examples

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

Step 1

Rewrite the equation as $2^{2 m - 9} = 32$ .

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

Step 2

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

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

Step 3

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

$2 m - 9 = 5$

Step 4

Solve for $m$ .

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Step 4.1

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

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Step 4.1.1

Add $9$ to both sides of the equation.

$2 m = 5 + 9$

Step 4.1.2

Add $5$ and $9$ .

$2 m = 14$

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $m$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $14$ by $2$ .

$m = 7$