Finite Math Examples

$9^{x + 2} = 240 + 9^{x}$

Step 1

Factor out $9^{x}$ from the expression.

$9^{x} (81 - 1)$

Step 2

Subtract $9^{x}$ from both sides of the equation.

$9^{x + 2} - 9^{x} = 240$

Step 3

Subtract $1$ from $81$ .

$9^{x} \cdot 80 = 240$

Step 4

Move $80$ to the left of $9^{x}$ .

$80 \cdot 9^{x} = 240$

Step 5

Divide each term in $80 \cdot 9^{x} = 240$ by $80$ and simplify.

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Step 5.1

Divide each term in $80 \cdot 9^{x} = 240$ by $80$ .

$\frac{80 \cdot 9^{x}}{80} = \frac{240}{80}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $80$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{80 \cdot 9^{x}}{80} = \frac{240}{80}$

Step 5.2.1.2

Divide $9^{x}$ by $1$ .

$9^{x} = \frac{240}{80}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $240$ by $80$ .

$9^{x} = 3$

Step 6

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

$3^{2 x} = 3^{1}$

Step 7

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

$2 x = 1$

Step 8

Divide each term in $2 x = 1$ by $2$ and simplify.

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Step 8.1

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $2$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$