Algebra Examples

$\frac{1}{2} {(3)}^{x} = \frac{9}{2}$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot 3^{x}) = 2 (\frac{9}{2})$

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $2 (\frac{1}{2} \cdot 3^{x})$ .

Tap for more steps...

Step 2.1.1.1

Combine $\frac{1}{2}$ and $3^{x}$ .

$2 \frac{3^{x}}{2} = 2 (\frac{9}{2})$

Step 2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{3^{x}}{2} = 2 (\frac{9}{2})$

Step 2.1.1.2.2

Rewrite the expression.

$3^{x} = 2 (\frac{9}{2})$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$3^{x} = 2 (\frac{9}{2})$

Step 2.2.1.2

Rewrite the expression.

$3^{x} = 9$

Step 3

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

$3^{x} = 3^{2}$

Step 4

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

$x = 2$