Finite Math Examples

$3^{5 x - 5} = 81$

Step 1

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

$3^{5 x - 5} = 3^{4}$

Step 2

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

$5 x - 5 = 4$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Add $5$ to both sides of the equation.

$5 x = 4 + 5$

Step 3.1.2

Add $4$ and $5$ .

$5 x = 9$

Step 3.2

Divide each term in $5 x = 9$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 x = 9$ by $5$ .

$\frac{5 x}{5} = \frac{9}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{9}{5}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{5}$

Decimal Form:

$x = 1.8$

Mixed Number Form:

$x = 1 \frac{4}{5}$