Algebra Examples

$8 \cdot 3^{n - 1} - 21 = 51$

Step 1

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

Tap for more steps...

Step 1.1

Add $21$ to both sides of the equation.

$8 \cdot 3^{n - 1} = 51 + 21$

Step 1.2

Add $51$ and $21$ .

$8 \cdot 3^{n - 1} = 72$

Step 2

Divide each term in $8 \cdot 3^{n - 1} = 72$ by $8$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $8 \cdot 3^{n - 1} = 72$ by $8$ .

$\frac{8 \cdot 3^{n - 1}}{8} = \frac{72}{8}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{8 \cdot 3^{n - 1}}{8} = \frac{72}{8}$

Step 2.2.1.2

Divide $3^{n - 1}$ by $1$ .

$3^{n - 1} = \frac{72}{8}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $72$ by $8$ .

$3^{n - 1} = 9$

Step 3

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

$3^{n - 1} = 3^{2}$

Step 4

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

$n - 1 = 2$

Step 5

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

Tap for more steps...

Step 5.1

Add $1$ to both sides of the equation.

$n = 2 + 1$

Step 5.2

Add $2$ and $1$ .

$n = 3$