Algebra Examples

81^{x} = 3

$81^{x} = 3$

Step 1

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

3^{4 x} = 3^{1}

$3^{4 x} = 3^{1}$

Step 2

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

4 x = 1

$4 x = 1$

Step 3

Divide each term in

4 x = 1

$4 x = 1$ by

4

$4$ and simplify.

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Step 3.1

Divide each term in

4 x = 1

$4 x = 1$ by

4

$4$ .

\frac{4 x}{4} = \frac{1}{4}

$\frac{4 x}{4} = \frac{1}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

4

$4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Step 3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}$

Decimal Form:

$x = 0.25$

$81^{x} = 3$

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