Finite Math Examples

$8^{x} = 16^{3 x + 9}$

Step 1

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

$2^{3 x} = 2^{4 (3 x + 9)}$

Step 2

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

$3 x = 4 (3 x + 9)$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Simplify $4 (3 x + 9)$ .

Tap for more steps...

Step 3.1.1

Apply the distributive property.

$3 x = 4 (3 x) + 4 \cdot 9$

Step 3.1.2

Multiply.

Tap for more steps...

Step 3.1.2.1

Multiply $3$ by $4$ .

$3 x = 12 x + 4 \cdot 9$

Step 3.1.2.2

Multiply $4$ by $9$ .

$3 x = 12 x + 36$

Step 3.2

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.2.1

Subtract $12 x$ from both sides of the equation.

$3 x - 12 x = 36$

Step 3.2.2

Subtract $12 x$ from $3 x$ .

$- 9 x = 36$

Step 3.3

Divide each term in $- 9 x = 36$ by $- 9$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 9 x = 36$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{36}{- 9}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 9$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{36}{- 9}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{36}{- 9}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $36$ by $- 9$ .

$x = - 4$