Basic Math Examples

$2^{2 n + 1} = 32$

Step 1

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

$2^{2 n + 1} = 2^{5}$

Step 2

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

$2 n + 1 = 5$

Step 3

Solve for

$n$ .

Tap for more steps...

Step 3.1

Move all terms not containing

$n$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Subtract

$1$ from both sides of the equation.

$2 n = 5 - 1$

Step 3.1.2

Subtract

$1$ from

$5$ .

$2 n = 4$

Step 3.2

Divide each term in

$2 n = 4$ by

$2$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in

$2 n = 4$ by

$2$ .

$\frac{2 n}{2} = \frac{4}{2}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 n}{2} = \frac{4}{2}$

Step 3.2.2.1.2

Divide

$n$ by

$1$ .

$n = \frac{4}{2}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide

$4$ by

$2$ .

$n = 2$