Algebra Examples

$3^{2 x} = 81$

Step 1

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

$3^{2 x} = 3^{4}$

Step 2

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

$2 x = 4$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $4$ by $2$ .

$x = 2$