Precalculus Examples

$4^{x + 7} = 8^{x + 3}$

Step 1

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

$2^{2 (x + 7)} = 2^{3 (x + 3)}$

Step 2

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

$2 (x + 7) = 3 (x + 3)$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Simplify $2 (x + 7)$ .

Tap for more steps...

Step 3.1.1

Rewrite.

$0 + 0 + 2 (x + 7) = 3 (x + 3)$

Step 3.1.2

Simplify by adding zeros.

$2 (x + 7) = 3 (x + 3)$

Step 3.1.3

Apply the distributive property.

$2 x + 2 \cdot 7 = 3 (x + 3)$

Step 3.1.4

Multiply $2$ by $7$ .

$2 x + 14 = 3 (x + 3)$

Step 3.2

Simplify $3 (x + 3)$ .

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$2 x + 14 = 3 x + 3 \cdot 3$

Step 3.2.2

Multiply $3$ by $3$ .

$2 x + 14 = 3 x + 9$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Subtract $3 x$ from both sides of the equation.

$2 x + 14 - 3 x = 9$

Step 3.3.2

Subtract $3 x$ from $2 x$ .

$- x + 14 = 9$

Step 3.4

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

Tap for more steps...

Step 3.4.1

Subtract $14$ from both sides of the equation.

$- x = 9 - 14$

Step 3.4.2

Subtract $14$ from $9$ .

$- x = - 5$

Step 3.5

Divide each term in $- x = - 5$ by $- 1$ and simplify.

Tap for more steps...

Step 3.5.1

Divide each term in $- x = - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 5}{- 1}$

Step 3.5.2

Simplify the left side.

Tap for more steps...

Step 3.5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 5}{- 1}$

Step 3.5.2.2

Divide $x$ by $1$ .

$x = \frac{- 5}{- 1}$

Step 3.5.3

Simplify the right side.

Tap for more steps...

Step 3.5.3.1

Divide $- 5$ by $- 1$ .

$x = 5$