Algebra Examples

$3 = 81^{x}$

Step 1

Rewrite the equation as $81^{x} = 3$ .

$81^{x} = 3$

Step 2

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

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

Step 3

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

$4 x = 1$

Step 4

Divide each term in $4 x = 1$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x = 1$ by $4$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.25$