Algebra Examples

$27^{2 x} = 9^{x + 1}$

Step 1

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

$3^{3 (2 x)} = 3^{2 (x + 1)}$

Step 2

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

$3 (2 x) = 2 (x + 1)$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Multiply $2$ by $3$ .

$6 x = 2 (x + 1)$

Step 3.2

Simplify $2 (x + 1)$ .

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$6 x = 2 x + 2 \cdot 1$

Step 3.2.2

Multiply $2$ by $1$ .

$6 x = 2 x + 2$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Subtract $2 x$ from both sides of the equation.

$6 x - 2 x = 2$

Step 3.3.2

Subtract $2 x$ from $6 x$ .

$4 x = 2$

Step 3.4

Divide each term in $4 x = 2$ by $4$ and simplify.

Tap for more steps...

Step 3.4.1

Divide each term in $4 x = 2$ by $4$ .

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

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor.

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

Step 3.4.2.1.2

Divide $x$ by $1$ .

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

Step 3.4.3

Simplify the right side.

Tap for more steps...

Step 3.4.3.1

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 3.4.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Step 3.4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.4.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 3.4.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 3.4.3.1.2.3

Rewrite the expression.

$x = \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$